Research on the singularities of a variety

• Project/Area Number: 18340004
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Algebra
• Research Institution: Tokyo Institute of Technology
• Principal Investigator: ISHII Shihoko Tokyo Institute of Technology, 大学院・理工学研究科, 教授 (60202933)
• Co-Investigator(Kenkyū-buntansha): TOMARI Masataka 日本大学, 文理学部, 教授 (60183878) ; FUJITA Takao 東京工業大学, 大学院・理工学研究科, 教授 (40092324) ; WATANABE Keiichi 日本大学, 文理学部, 教授 (10087083) ; TOMARU Tadashi 群馬大学, 医学部, 教授 (70132579)
• Project Period (FY): 2006 – 2009
• Project Status: Completed (Fiscal Year 2009)
• Budget Amount: ¥14,610,000 (Direct Cost: ¥11,700,000、Indirect Cost: ¥2,910,000); Fiscal Year 2009: ¥5,200,000 (Direct Cost: ¥4,000,000、Indirect Cost: ¥1,200,000); Fiscal Year 2008: ¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000); Fiscal Year 2007: ¥5,200,000 (Direct Cost: ¥4,000,000、Indirect Cost: ¥1,200,000); Fiscal Year 2006: ¥2,000,000 (Direct Cost: ¥2,000,000)
• Keywords: 特異点 / 弧空間 / ジェットスキーム / 双有理幾何学 / ジェット空間 / lc-threshold / singularity / integrally closed ideal / jet scheme / arc space / log-canonical threshold / integnally closedjlul

Research Abstract

We clarified the relationship between some properties of singularities on a variety and the properties on the arc space and the jet schemes over the variety. We gave a characterization of the regularity of the base variety by the flatness of a truncation morphism of jet schemes. The relationship between degenerating families of algebraic curves and two dimensional singularities. We introduced F-threshold for pair of ideals in commutative rings by means of positive characteristic method and generalized the formula on multiplicity.

Research Products

• [Journal Article] Geometric properties of jet schemes (2011)
  • Author(s): S.Ishii
  • Journal Title: Comm.in Alg. in press
  • Peer Reviewed
• [Journal Article] Multiplicity bounds in graded rings (2011)
  • Author(s): K.Watanabe, C.Huneke, S.Takagi
  • Journal Title: Kyoto Journal of Mathematics. in press
  • Peer Reviewed
• [Journal Article] Pseudo-symmetric and atomic numerical semigroups generated by three elements (2011)
  • Author(s): K.Watanabe, H.Nari, T.Numata
  • Journal Title: Proc.Inst.Natural Sci., Nihon Univ. 46 in press
  • Peer Reviewed
• [Journal Article] F-signature of graded Gorenstein rings (2011)
  • Author(s): K.Watanabe, A.Sannai
  • Journal Title: J.Pure and Appl.Algebra. in press
  • Peer Reviewed
• [Journal Article] Coefficient ideal of ideals generated by monomials (2011)
  • Author(s): K.Watanabe, S.Ohnishi
  • Journal Title: Communications in Algebra. in press
  • Peer Reviewed
• [Journal Article] Geometric properties of jet schemes (2011)
  • Author(s): S.Ishii
  • Journal Title: Comm.in Alg. Volume: (in press)
  • Peer Reviewed
• [Journal Article] Coefficient ideal of ideals generated by monomials (2011)
  • Author(s): K.Watanabe (S.Ohnishi)
  • Journal Title: Communications in Algebra Volume: (in press)
  • Peer Reviewed
• [Journal Article] F-signature of graded Gorenstein rings (2011)
  • Author(s): K.Watanabe (A.Sannai)
  • Journal Title: J.Pure and Appl.Algebra Volume: (in press)
  • Peer Reviewed
• [Journal Article] Pseudo-symmetric and atomic numerical semigroups generated by three elements (2011)
  • Author(s): K.Watanabe (H.Nari, T.Numata)
  • Journal Title: Proc.Inst.Natural Sci., Nihon Univ. Volume: 46(in press)
  • Peer Reviewed
• [Journal Article] Multiplicity bounds in graded rings (2011)
  • Author(s): K.Watanabe (C.Huneke, S.Takagi)
  • Journal Title: Kyoto Journal of Mathematics Volume: (in press)
  • Peer Reviewed
• [Journal Article] Nash problem for a toric pair and the minimal log-discrepancy (2010)
  • Author(s): S.Ishii
  • Journal Title: Comptes Rendus Math.Acad.Sci.Paris 348 Pages: 985-988
  • Peer Reviewed
• [Journal Article] Isomorphisms of jet schemes Comptes Rendus Math. (2010)
  • Author(s): S.Ishii
  • Journal Title: Rep.Acad.Sci.Canada. 32 Pages: 19-23
  • Peer Reviewed
• [Journal Article] Complex surface singularities and degenerations of compact complex curves (2010)
  • Author(s): T.Tomaru
  • Journal Title: Demonstratio Mathematica 43(2) Pages: 39-59
  • Peer Reviewed
• [Journal Article] Isomorphisms of jet schemes (2010)
  • Author(s): S.Ishii
  • Journal Title: Comptes Rendus Math.Rep.Acad.Sci.Canada. Volume: 32 Pages: 19-23
  • Peer Reviewed
• [Journal Article] Nash problem for a toric pair and the minimal log-discrepancy (2010)
  • Author(s): S.Ishii
  • Journal Title: Comptes Rendus Math.Acad.Sci.Paris Volume: 348 Pages: 985-988
  • Peer Reviewed
• [Journal Article] Complex surface singularities and degenerations of compact complex curves (2010)
  • Author(s): T.Tomaru
  • Journal Title: Demonstratio Mathematica Volume: 43(2) Pages: 39-59
  • Peer Reviewed
• [Journal Article] Smoothness and jet schemes (2009)
  • Author(s): S.Ishii
  • Journal Title: Adv.St.Pure Math. 56 Pages: 187-199
  • Peer Reviewed
• [Journal Article] Multigraded rings, diagonal subalgebras, and rational singularities (2009)
  • Author(s): K.Watanabe, K.Kurano, E.Sato, A.Singh
  • Journal Title: J.of Algebra 322 Pages: 3248-3267
  • Peer Reviewed
• [Journal Article] Smoothness and jet schemes (2009)
  • Author(s): S.Ishii
  • Journal Title: Adv.St.Pure Math. Volume: 56 Pages: 187-199
  • Peer Reviewed
• [Journal Article] Multigraded rings, diagonal subalgebras, and rational singularities (2009)
  • Author(s): K.Watanabe (K.Kurano, E.Sato, A.Singh)
  • Journal Title: J.of Algebra Volume: 322 Pages: 3248-3267
  • Peer Reviewed
• [Journal Article] Smoothness and jet schemes (2009)
  • Author(s): Shihoko Ishii
  • Journal Title: Advanced Studies in Pure Mathematics (In Press)
  • Peer Reviewed
• [Journal Article] Complex surface singularities and degenerations of compact complex curves (2009)
  • Author(s): Tadashi Tomaru
  • Journal Title: Demonstratio Math (In Press)
  • Peer Reviewed
• [Journal Article] Divisorial valuations via arcs (2008)
  • Author(s): S.Ishii, T.De Fernex, L.Ein
  • Journal Title: Publ.RIMS 44 Pages: 425-448
  • NAID: 110006648219
  • Peer Reviewed
• [Journal Article] Maximal divisorial sets in arc spaces (2008)
  • Author(s): S.Ishii
  • Journal Title: Adv.St.Pure Math. 50 Pages: 237-249
  • Peer Reviewed
• [Journal Article] Coefficient ideals of ideals in $k[X, Y]$ generated by monomials (2008)
  • Author(s): K.Watanabe, S.Ohnishi
  • Journal Title: Proc.Inst.Natural Sci., Nihon Univ. 43 Pages: 347-352
  • Peer Reviewed
• [Journal Article] F-thresholds, tight closure, integral closure, and multiplicity bounds (2008)
  • Author(s): K.Watanabe, C.Huneke, M.Mustata, S.Takagi
  • Journal Title: Michigan Math.J. 57 Pages: 463-483
  • Peer Reviewed
• [Journal Article] Divisorial valuations viaarcs (2008)
  • Author(s): Tommaso de Fernex, Lawrence Ein and Shihoko Ishii
  • Journal Title: Publ. RIMS, Kyoto Univ. 44 Pages: 425-448
  • NAID: 110006648219
  • Peer Reviewed
• [Journal Article] F-thresholds, tight closure, integral closure, and multiplicity bounds (2008)
  • Author(s): C. Huneke, M. Mustata, S. Takagi and K. Watanabe
  • Journal Title: Michigan Math. J. 57 Pages: 463-483
  • Peer Reviewed
• [Journal Article] Divisorial valuations via arcs (2008)
  • Author(s): Tommaso de Fernex, Lawrence Ein, Shihoko Ishii
  • Journal Title: Publ. RIMS, Kyoto Univ. 44 Pages: 425-448
  • NAID: 110006648219
  • Peer Reviewed
• [Journal Article] F-thresholds, tight closure, integral closure, and multiplicity bounds (2008)
  • Author(s): C. Huneke, M. Mustata, S. Takagi, K. Watanabe
  • Journal Title: Michigan Math. J. 57
  • Peer Reviewed
• [Journal Article] Maximal divisorial sets in arc spaces (2008)
  • Author(s): 石井志保子
  • Journal Title: Adv. St. Pure Math. 50 Pages: 237-249
  • Peer Reviewed
• [Journal Article] Divisorial valuations via arcs (2008)
  • Author(s): 石井志保子 T. De Fernex, L. Ein
  • Journal Title: to appear in Publ. RIMS (掲載決定)
  • NAID: 110006648219
  • Peer Reviewed
• [Journal Article] F-thresholds, tight closure, integral closure, and multiplicity bounds (2008)
  • Author(s): 渡辺敬一, C. Huneke, M. Mustata and S, Takagi
  • Journal Title: to appear in Michigan Math. J. (掲載決定)
  • Peer Reviewed
• [Journal Article] Coefficient ideals of ideals in $k[X,Y]$ generated by monomials (2008)
  • Author(s): 渡辺敬一
  • Journal Title: to appear in Proc. Inst. Natural Sci., Nihon Univ. 43(掲載決定)
  • Peer Reviewed
• [Journal Article] Jet schemes, arc spaces and the Nash problem (2007)
  • Author(s): S.Ishii
  • Journal Title: C.R.Math.Rep.Acad.Canada 29 Pages: 1-21
  • Peer Reviewed
• [Journal Article] Totally reflexive modules constructed from smooth projective curves of genus $g\geq2$ (2007)
  • Author(s): K.Watanabe, R.Takahashi
  • Journal Title: Archiv der Mathematik 89 Pages: 60-67
  • Peer Reviewed
• [Journal Article] Pencil genus for normal surface singularities (2007)
  • Author(s): T.Tomaru
  • Journal Title: J.Math.Soc.Japan 59(1) Pages: 35-80
  • NAID: 10019540487
  • Peer Reviewed
• [Journal Article] Jet schemes, arc spaces and the Nash problem (2007)
  • Author(s): 石井志保子
  • Journal Title: C. R. Math. Rep. Acad. Sci. Canada 29 Pages: 1-21
  • Peer Reviewed
• [Journal Article] Totally reflexive modules constructed from smooth projective curves of genus (2007)
  • Author(s): 渡辺敬一
  • Journal Title: Archiv der Mathematik 89 Pages: 60-67
  • Peer Reviewed
• [Journal Article] The local Nash problem on arc families of singularities (2006)
  • Author(s): S.Ishii
  • Journal Title: Annales de L'Institut Fourier. 56 Pages: 1207-1224
  • Peer Reviewed
• [Journal Article] Adjacent integrally closed ideals in 2-dimensional regular local rings (2006)
  • Author(s): K.Watanabe, S.Noh
  • Journal Title: J.of Algebra 302 Pages: 156-166
  • Peer Reviewed
• [Journal Article] 代数曲線のC^*-作用をもつ退化族と2次元擬斉次特異点 (2006)
  • Author(s): T.Tomaru
  • Journal Title: 第2回トポロジー・代数幾何玉原セミナー報告集 Pages: 1-19
  • Peer Reviewed
• [Journal Article] The local Nasl problem on arc families of singularities (2006)
  • Author(s): 石井志保子
  • Journal Title: Annales de L'institut Fourier 56 Pages: 1207-1224
• [Journal Article] Adjacent integrally dosed idecls in 2-dimeasinul regular localrin (2006)
  • Author(s): 渡辺敬一, S. Noh
  • Journal Title: Joural of Algebra 302 Pages: 156-166
• [Journal Article] Smoothness and jet schemes
  • Author(s): Shihoko Ishii
  • Journal Title: Advanced Studies in Pure Mathematics (掲載決定)
  • Peer Reviewed
• [Journal Article] Complex surface singularities and degenerations of compact complex curves
  • Author(s): Tadashi Tomaru
  • Journal Title: Demonstratio Math (掲載決定)
  • Peer Reviewed
• [Journal Article] Maximal divisorial sits in arc spaces
  • Author(s): 石井志保子
  • Journal Title: Advanced St. Math. (掲載決定)
• [Journal Article] Jet schemes, arc spaces and the Nasl problem
  • Author(s): 石井志保子
  • Journal Title: Comptes Rendus Mathematiques (掲載決定)
• [Journal Article] Totally reflexive modulus construsded from projective curves of genus g22
  • Author(s): 渡辺敬一, 高橋良
  • Journal Title: Archiv der Mathematik (掲載決定)
• [Presentation] A positive characteristic approach to Wang's theorem (2010)
  • Author(s): K.Watanabe, K.Yoshida
  • Organizer: 32nd Commutative Algebra Symposium, 6th Japan-Vietnam Joint Seminar on Commutative Algebra
  • Place of Presentation: IPC生産性国際交流センター,葉山
  • Year and Date: 2010-12-06
• [Presentation] A variant of Wang's Theorem in positive characteristic (2010)
  • Author(s): K.Watanabe
  • Organizer: Commutative Algebra and its Interactions with Algebraic Geometry
  • Place of Presentation: C.I.R.M, Luminy
  • Year and Date: 2010-11-05
• [Presentation] Usual discrepancy versus Mather discrepancy (2010)
  • Author(s): S.Ishii
  • Organizer: 特異点と多様体の幾何学
  • Place of Presentation: 山形大学
  • Year and Date: 2010-09-17
• [Presentation] Usual discrepancy versus Mather discrepancy (2010)
  • Author(s): S.Ishii
  • Organizer: 研究集会「特異点と多様体の幾何学」
  • Place of Presentation: 山形大学
  • Year and Date: 2010-09-17
• [Presentation] 特異点の問題 (2010)
  • Author(s): S.Ishii
  • Organizer: 複素幾何学の諸問題
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2010-09-07
• [Presentation] 特異点の問題 (2010)
  • Author(s): S.Ishii
  • Organizer: RIMS共同研究集会「複素幾何学の諸問題」
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2010-09-07
• [Presentation] Mather discrepancy and arc spaces (2010)
  • Author(s): S.Ishii
  • Organizer: Algebraic Geometry and its Applications Abhyankar's 80th birthday Conference
  • Place of Presentation: Purdue University
  • Year and Date: 2010-07-21
• [Presentation] Some topics on F-thresholds (2010)
  • Author(s): K.Watanabe
  • Organizer: Workshop on Local Rings and Local Study of Algebraic Varieties
  • Place of Presentation: ICTP Trieste
  • Year and Date: 2010-06-07
• [Presentation] Some topics on F-thresholds (2010)
  • Author(s): K.Watanabe
  • Organizer: Frobenius splitting conferrence
  • Place of Presentation: Michigan University, Ann Arbor
  • Year and Date: 2010-05-18
• [Presentation] Some topics on F-thresholds (2010)
  • Author(s): K.Watanabe
  • Organizer: Frobenius splitting conference
  • Place of Presentation: Michigan University, Ann Arbor
  • Year and Date: 2010-05-18
• [Presentation] Some topics on F-thresholds (2010)
  • Author(s): K.Watanabe
  • Organizer: Juergan Herzogを囲む可換代数の集い
  • Place of Presentation: 大阪大学
  • Year and Date: 2010-01-28
• [Presentation] Some topics on F-thresholds (2010)
  • Author(s): K.Watanabe
  • Organizer: The 5-th Japan-Vietnam Joint Seminar on Commutative Algebra
  • Place of Presentation: Hanoi
  • Year and Date: 2010-01-05
• [Presentation] The $a$ invariants of normal graded Gorenstein rings and varieties with even canonical class (2009)
  • Author(s): K.Watanabe
  • Organizer: 第31回可換環論シンポジウム
  • Place of Presentation: アウィーナ大阪
  • Year and Date: 2009-11-25
• [Presentation] Isomorphism problem on jet schemes (2009)
  • Author(s): S.Ishii
  • Organizer: Invariants in Algebraic Geometry
  • Place of Presentation: 東京大学
  • Year and Date: 2009-11-13
• [Presentation] The $a$ invariants of normal graded Gorenstein rings and varieties with even canonical class (2009)
  • Author(s): K.Watanabe
  • Organizer: 日本数学会一般講演
  • Place of Presentation: 大阪大学
  • Year and Date: 2009-09-26
• [Presentation] The $a$ invariants of normal graded Gorenstein rings and varieties with even canonical class (2009)
  • Author(s): K.Watanabe
  • Organizer: 日本数学会
  • Place of Presentation: 大阪大学
  • Year and Date: 2009-09-26
• [Presentation] From jet schemes to the base scheme-Isomorphism problems (global and local)- (2009)
  • Author(s): S.Ishii
  • Organizer: Workshop on Singularities
  • Place of Presentation: Oberwolfach
  • Year and Date: 2009-09-25
• [Presentation] From jet schemes to the base scheme--Isomorphism problems (global and local)-- (2009)
  • Author(s): S.Ishii
  • Organizer: Workshop on Singularities
  • Place of Presentation: Oberwolfach
  • Year and Date: 2009-09-25
• [Presentation] From jet schemes to the base scheme (2009)
  • Author(s): S.Ishii
  • Organizer: Austrarian-Japanese Workshop on Real and Complex Singularities
  • Place of Presentation: Sydney University
  • Year and Date: 2009-09-16
• [Presentation] Singularities on jet schemes (2009)
  • Author(s): S.Ishii
  • Organizer: Fifth Franco-Japanese Symposium on Singularities
  • Place of Presentation: Strasbourg University
  • Year and Date: 2009-08-27
• [Presentation] C*-degenerations of compact complex curves and cyclic covers of normal C*-surface singularities (2009)
  • Author(s): T.Tomaru
  • Organizer: Singularities in Aarhus
  • Place of Presentation: Aarhus, Denmark
  • Year and Date: 2009-08-20
• [Presentation] C^*-degenerations of compact complex curves and cyclic covers of normal C^*-surface singularities (2009)
  • Author(s): T.Tomaru
  • Organizer: Singularities in Aarhus
  • Place of Presentation: Aarhus, Denmark
  • Year and Date: 2009-08-20
• [Presentation] The a invariants of normal graded Gorenstein rings and varieties with even canonical class (2009)
  • Author(s): K.Watanabe
  • Organizer: PASI 2009, Commutative Algebra and its connections to Geometry
  • Place of Presentation: Olinda, Brazil
  • Year and Date: 2009-08-14
• [Presentation] a-invariant of normal graded Gorenstein domains and varieties with even canonical class (2009)
  • Author(s): K.Watanabe
  • Organizer: 2009 PRIMA congress
  • Place of Presentation: University of New South Wales, Sydney
  • Year and Date: 2009-07-08
• [Presentation] a-invariant of normal graded Gorenstein domains and varieties with even canonical class (2009)
  • Author(s): K.Watanabe
  • Organizer: Kommutative Algebra
  • Place of Presentation: Oberwolfach
  • Year and Date: 2009-04-24
• [Presentation] a-invariant of normal graded Gorenstein domains and varieties with even canonical class (2009)
  • Author(s): K.Watanabe
  • Organizer: Commutative Algebra
  • Place of Presentation: Oberwolfach
  • Year and Date: 2009-04-24
• [Presentation] Geometric properties of jet schemes (2009)
  • Author(s): S.Ishii
  • Organizer: Harvard-MIT Algebraic Geometry Seminar
  • Place of Presentation: Harvard University
  • Year and Date: 2009-03-17
• [Presentation] Geometric properties of jet schemes (2009)
  • Author(s): S.Ishii
  • Organizer: Main Seminar at MSRI
  • Place of Presentation: Berkeley, California
  • Year and Date: 2009-03-09
• [Presentation] From jet schemes to the base scheme (2009)
  • Author(s): Shihoko Ishii
  • Organizer: Main Seminar in Algebraic Geometry
  • Place of Presentation: MSRI(Mathematical Science Research Institute, Berkeley)
  • Year and Date: 2009-03-09
• [Presentation] From jet schemes to the base scheme (2009)
  • Author(s): Shihoko Ishii
  • Organizer: Main Seminar in Algebraic Geometry
  • Place of Presentation: MSRI (Mathematical Science Research Institute, Berkeley)
  • Year and Date: 2009-03-09
• [Presentation] Hilbert-Kunz multiplicities (2009)
  • Author(s): K.Watanabe
  • Organizer: Mini Workshop of Algebra
  • Place of Presentation: Taiwan National University
• [Presentation] C*-作用をもつリーマン面の退化族とC*-作用をもつ2次元特異点 (2008)
  • Author(s): T.Tomaru
  • Organizer: 多変数函数論冬セミナー
  • Place of Presentation: 熊本大学理学部
  • Year and Date: 2008-12-24
• [Presentation] Coefficient ideals of monomial idelas (2008)
  • Author(s): K.Watanabe
  • Organizer: 第30回可換環論シンポジウム
  • Place of Presentation: 唐津
  • Year and Date: 2008-11-19
• [Presentation] Classification of 2-dimensional normal graded hypersurfaces with small a-invariants (2008)
  • Author(s): K.Watanabe
  • Organizer: Algebre commutative et ses interactions avec la geometrie algebrique
  • Place of Presentation: C.I.R.M.
  • Year and Date: 2008-10-01
• [Presentation] Classification of 2-dimensional normal graded hypersurfaces with small a-invariants (2008)
  • Author(s): K.Watanabe
  • Organizer: Algebra Workshop
  • Place of Presentation: Kansas Univ.
  • Year and Date: 2008-07-25
• [Presentation] Geometric properties by jet schemes (2008)
  • Author(s): S.Ishii
  • Organizer: Hayama Symposium on Complex Analysis in Several Variables XII
  • Place of Presentation: 葉山国際村センター
  • Year and Date: 2008-07-15
• [Presentation] 複素2次元特異点と閉リーマン面の退化族について (2008)
  • Author(s): T.Tomaru
  • Organizer: 日本数学会
  • Place of Presentation: 近畿大学
  • Year and Date: 2008-03-24
• [Presentation] 複素2次元特異点と閉リーマン面の退化族について (2008)
  • Author(s): 都丸正
  • Organizer: 日本数学会総合分科会関数論部会特別講演
  • Place of Presentation: 近畿大学
  • Year and Date: 2008-03-23
• [Presentation] Methods of characteristic p>0 in Singularity Theory (2008)
  • Author(s): K.Watanabe
  • Organizer: 第3回代数・解析・幾何セミナー
  • Place of Presentation: 鹿児島大学
  • Year and Date: 2008-02-18
• [Presentation] Methods of characteristic $p>0$ in Singularity Theory (2008)
  • Author(s): 渡辺敬一
  • Organizer: 第3回代数・解析・幾何セミナー
  • Place of Presentation: 鹿児島大学2/18-21
  • Year and Date: 2008-02-18
• [Presentation] Toric varieties, monomial valuations and arc spaces (2008)
  • Author(s): S.Ishii
  • Organizer: トーリック多様体の理論の展開と応用
  • Place of Presentation: 東北大学
  • Year and Date: 2008-01-10
• [Presentation] F-thresholds, with applications to multiplier ideals, intgral closure and multiplicity (2008)
  • Author(s): K.Watanabe
  • Organizer: Cimpa Conference on Commutative Algebra
  • Place of Presentation: IIT Bombay, Mumbai, India
  • Year and Date: 2008-01-10
• [Presentation] Toric varieties, monomial valuations and arc spaces. (2008)
  • Author(s): 石井志保子
  • Organizer: 研究集会「トーリック多様体の理論の展開と応用」
  • Place of Presentation: 東北大学
  • Year and Date: 2008-01-10
• [Presentation] F-thresholds, with applications to multiplier ideals, integral closure and multiplicity (2008)
  • Author(s): 渡辺敬一
  • Organizer: CIMPA Conference on Commutative Algebra
  • Place of Presentation: IIT Bombay, Mumbai, India
  • Year and Date: 2008-01-10
• [Presentation] Introduction to arc spaces and the Nash problem (2008)
  • Author(s): S.Ishii
  • Organizer: Fourth meeting for Young Mathematicians in Sedano
  • Place of Presentation: Sedano, Spain
• [Presentation] Introduction to arc spaces and the Nash problem. (2008)
  • Author(s): 石井志保子
  • Organizer: Fourth meeting for Young Mathematicians in Sedano (8時間の連続講義)
  • Place of Presentation: Sedano, Spain
• [Presentation] Smoothness criteria by jet schemes (2007)
  • Author(s): S.Ishii
  • Organizer: Algebraic Geometry and Commutative Algebra Tokyo 2007
  • Place of Presentation: 東京大学
  • Year and Date: 2007-12-13
• [Presentation] Smoothness criteria by jet schemes. (2007)
  • Author(s): 石井志保子
  • Organizer: Algebraic Geometry and Commutative Algebra Tokyo 2007
  • Place of Presentation: 東京大学
  • Year and Date: 2007-12-13
• [Presentation] F-thresholds-application to lc thresholds and a conjecture on multiplicity (2007)
  • Author(s): K.Watanabe
  • Organizer: Algebraic Geometry and Commutative Algebra Tokyo 2007
  • Place of Presentation: 東京大学
  • Year and Date: 2007-12-12
• [Presentation] F-thresholds - application to lc thresholds and a conjecture on multiplicity (2007)
  • Author(s): 渡辺敬一
  • Organizer: Algebraic Geometry and Commutative Algebra Tokyo 2007
  • Place of Presentation: 東京大学
  • Year and Date: 2007-12-12
• [Presentation] Classification of $2$-dimensional normal graded hypersurfaces with $a(R)=1$ (2007)
  • Author(s): K.Watanabe
  • Place of Presentation: Palo Alto
  • Year and Date: 2007-11-22
• [Presentation] F-thresholds, tight closure, integral closure and multiplicity bounds (2007)
  • Author(s): K.Watanabe, C.Huneke, M.Mustata, S.Takagi
  • Organizer: 第29回可換環論シンポジウム
  • Place of Presentation: 名古屋・池下厚生年金会館
  • Year and Date: 2007-11-19
• [Presentation] F-thresholds, tight closure, integral closure and multiplicity bounds (with C. Huneke, M. Mustata, S. Takagi) (2007)
  • Author(s): 渡辺敬一
  • Organizer: 第29回可換環論シンポジウム
  • Place of Presentation: 名古屋・池下厚生年金会館
  • Year and Date: 2007-11-19
• [Presentation] Arcs and valuations-some finiteness properties- (2007)
  • Author(s): S.Ishii
  • Organizer: 城崎代数幾何学シンポジウム
  • Place of Presentation: 城崎大会議館
  • Year and Date: 2007-10-26
• [Presentation] Arcs and valuations-some finiteness properties (2007)
  • Author(s): 石井志保子
  • Organizer: 城崎代数幾何学シンポジウム
  • Place of Presentation: 城崎大会議館
  • Year and Date: 2007-10-26
• [Presentation] C*-作用をもつリーマン面の退化族とC*-作用をもつ2次元特異点 (2007)
  • Author(s): T.Tomaru
  • Organizer: 日本数学会
  • Place of Presentation: 東北大学
  • Year and Date: 2007-09-24
• [Presentation] C^<*->作用をもつリーマン面の退化族とC^<*->作用をもつ2次元特異点 (2007)
  • Author(s): 都丸正
  • Organizer: 日本数学会秋季総合分科会関数論部会一般講演
  • Place of Presentation: 東北大学
  • Year and Date: 2007-09-24
• [Presentation] Ring theoretic properties of F-thresholds (2007)
  • Author(s): K.Watanabe
  • Organizer: Hilbert Functions and Syzygies in Commutative Algebra and Combinatorics ; A conference in honor of Juergen Herzog on the occasion of his 65^<th> birthday
  • Place of Presentation: Cortona, Italy
  • Year and Date: 2007-09-18
• [Presentation] Ring theoretic properties of F-thresholds (2007)
  • Author(s): 渡辺敬一
  • Organizer: Hilbert functions and Syzygies in Commutative Algebra and Combinatrics: A Conference in honor of Juergen Herzog inthe occasion of his 65th birthday
  • Place of Presentation: Cortona, Italy
  • Year and Date: 2007-09-18
• [Presentation] Smoothness criteria by jet schemes (2007)
  • Author(s): S.Ishii
  • Organizer: Foruth Franco-Japanese Symposium on Singularities
  • Place of Presentation: 立山国際ホテル
  • Year and Date: 2007-08-28
• [Presentation] Smoothness criteria by jet schemes. (2007)
  • Author(s): 石井志保子
  • Organizer: Fourth Franco-Japanese Symposium on Singularities
  • Place of Presentation: 立山国際ホテル
  • Year and Date: 2007-08-28
• [Presentation] C*-Pencil of curves and C*-complex surface singualarities, Geometric Singularity Theory (2007)
  • Author(s): T.Tomaru
  • Organizer: Polish-Japanese Working Days
  • Place of Presentation: Poland, Sopot
  • Year and Date: 2007-07-12
• [Presentation] Methods of characteristic $p>0$ in Singularity Theory (2007)
  • Author(s): K.Watanabe
  • Organizer: Characteristic p methods in Algebraic Geometry
  • Place of Presentation: Drobeta-Turum-Severin ; Romania
• [Presentation] Methods of characteristic $p>0$ in Singularity Theory (2007)
  • Author(s): 渡辺敬一
  • Organizer: Summer School, "Characteristic p methods in Algebraic Geometry"(90分, 4回連続講演)
  • Place of Presentation: Drobeta-turum-Severin, Romania
• [Presentation] Ring theoretic properties of F-thresholds, Integral Closure (2006)
  • Author(s): K.Watanabe
  • Organizer: Multiplier Ideals and Cores
  • Place of Presentation: American Institute of Mathematics, Palo Alto
  • Year and Date: 2006-12-21
• [Presentation] Arcs and divisors (2006)
  • Author(s): S.Ishii
  • Organizer: Hayashibara Forum at IHES on Singularities
  • Place of Presentation: IHES Paris
  • Year and Date: 2006-11-21
• [Presentation] Some characteristic p methods for singularity theory (2006)
  • Author(s): K.Watanabe
  • Organizer: Workshop in Commutative Algebra
  • Place of Presentation: Univ.Essen
  • Year and Date: 2006-11-20
• [Presentation] Some Questions on F-thresholds (2006)
  • Author(s): K.Watanabe
  • Organizer: Meeting on Commutative Algebra ; Dedicated to the memory of Wilfgang Voge
  • Place of Presentation: Eisenach, Germany
  • Year and Date: 2006-11-19
• [Presentation] Introduction to jet schemes and arc spaces, I,II,III, IV (2006)
  • Author(s): S.Ishii
  • Organizer: Arc spaces and multiplier ideals
  • Place of Presentation: 京都大学数理解析研究所
• [Presentation] Multiplier ideals and arc spaces (2006)
  • Author(s): K.Watanabe
  • Place of Presentation: 京都大学数理解析研究所
• [Book] 運命のつながり-ガロワ理論-(この定理が美しい) (2009)
  • Author(s): S.Ishii
  • Publisher: 数学書房
• [Book] この定理が美しい (2009)
  • Author(s): 阿原一志, 石井志保子, 伊藤哲史, 伊藤由佳理, 牛瀧文宏, 大栗博司, 他全20名
  • Total Pages: 195
  • Publisher: 数学書房