A study on adjoint ideal sheaves by characteristic p methods

• Project/Area Number: 20740019
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: Algebra
• Research Institution: Kyushu University
• Principal Investigator: TAKAGI Shunsuke Kyushu University, 大学院・数理学研究院, 特任准教授 (40380670)
• Project Period (FY): 2008 – 2010
• Project Status: Completed (Fiscal Year 2010)
• Budget Amount: ¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000); Fiscal Year 2010: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2009: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000); Fiscal Year 2008: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
• Keywords: 代数幾何 / 可換環論 / 特異点論 / 代数幾何学 / 乗数イデアル層 / 密着閉包

Research Abstract

We introduced the notions of adjoint ideal sheaves and maximal non-lc ideal sheaves as analogs or variants of multiplier ideal sheaves, and then we studied their local properties by characteristic pmethods such as tight closure and Frobenius splitting. Also, we carried out a systematic study of invariants (F-jumping numbers, parameter F-jumping number, F-thresholds and non-F-pure ideals) related to test ideals, which can be viewed as a positive characteristic analog of multiplier ideal sheaves.

Research Products

• [Journal Article] Supplements to non-lc ideal sheaves (2011)
  • Author(s): Osamu Fujino, Karl Schwede, Shunsuke Takagi
  • Journal Title: RIMS Kokyuroku Bessatsu In Press
  • Peer Reviewed
• [Journal Article] Multiplicity bounds in graded rings (2011)
  • Author(s): Craig Huneke, Shunsuke Takagi, Kei-ichi Watanabe
  • Journal Title: Kyoto Journal of Mathematics 51 Pages: 127-147
  • Peer Reviewed
• [Journal Article] Multiplicity bounds in graded rings (2011)
  • Author(s): Craig Huneke, Shunsuke Takagi, Kei-ichi Watanabe
  • Journal Title: Kyoto Journal of Mathematics Volume: 51 Pages: 127-147
  • Peer Reviewed
• [Journal Article] Supplements to non-lc ideal sheaves (2011)
  • Author(s): Osamu Fujino, Karl Schwede, Shunsuke Takagi
  • Journal Title: RIMS Kokyuroku Bessatsu Volume: (In Press)
  • Peer Reviewed
• [Journal Article] Adjoint ideals along closed subvarieties of higher codimension (2010)
  • Author(s): Shunsuke Takagi
  • Journal Title: Journal furdie reine und angewandte Mathematik 641 Pages: 145-162
  • Peer Reviewed
• [Journal Article] Discreteness and rationality of F-jumping numbers on singular varieties (2010)
  • Author(s): Manuel Blickle, Karl Schwede, Shunsuke Takagi, Wenliang Zhang
  • Journal Title: 347 Pages: 917-949
  • Peer Reviewed
• [Journal Article] Adjoint ideals along closed subvarieties of higher codimension (2010)
  • Author(s): Shunsuke Takagi
  • Journal Title: Journal fur die reine und angewandte Mathematik Volume: 641 Pages: 145-162
  • Peer Reviewed
• [Journal Article] Discreteness and rationality of F-jumping numbers on singular varieties (2010)
  • Author(s): Manuel Blickle, Karl Schwede, Shunsuke Takagi, Wenliang Zhang
  • Journal Title: Mathematische Annalen Volume: 347 Pages: 917-949
  • Peer Reviewed
• [Journal Article] Adjoint ideals along closed subvarieties of higher codimension (2010)
  • Author(s): Shunsuke Takagi
  • Journal Title: Journal fur die reine und angewandte Mathematik (In Press)
  • Peer Reviewed
• [Journal Article] Discreteness and rationality of F-jumping numbers on singular varieties (2010)
  • Author(s): Manuel Buckle, Karl Schwede, Shunsuke Takagi, Wenliang Zhang
  • Journal Title: Mathematische Annalen (In Press)
  • Peer Reviewed
• [Journal Article] Adjoint ideals along closed subvarieties of higher codimension (2009)
  • Author(s): Shunsuke Takagi
  • Journal Title: Journal fur die reine and angewandte Mathematik (In Press)
  • Peer Reviewed
• [Presentation] Introduction to F-singularities (2010)
  • Author(s): Shunsuke Takagi
  • Organizer: Algebraic Geometry Seminar
  • Place of Presentation: POSTECH.
  • Year and Date: 2010-06-14
• [Presentation] Introduction to F-singularities (2010)
  • Author(s): Shunsuke Takagi
  • Organizer: Algebraic Geometry Seminar
  • Place of Presentation: POSTECH(韓国浦項市)
  • Year and Date: 2010-06-14
• [Presentation] Multiplicities and jumping numbers (2010)
  • Author(s): Shunsuke Takagi
  • Organizer: Algebraic Geometry in Characteristic p and Related Topics
  • Place of Presentation: 東京大学大学院数理科学研究科
  • Year and Date: 2010-02-18
• [Presentation] Multiplicities and jumping numbers. (2010)
  • Author(s): Shunsuke Takagi
  • Organizer: Algebraic Geometry in Characteristic p and Related Topics
  • Place of Presentation: 東京大学大学院数理科学研究科
  • Year and Date: 2010-02-18
• [Presentation] Log canonical thresholds of binomial ideals (2008)
  • Author(s): Shunsuke Takagi
  • Organizer: 第30回可換環論シンポジウム
  • Place of Presentation: 虹ノ松原ホテル(唐津市)
  • Year and Date: 2008-11-18
• [Presentation] Log canonical thresholds of binomial ideals (2008)
  • Author(s): Shunsuke Takagi
  • Organizer: 第30回可換環論シンポジウム
  • Place of Presentation: 虹ノ松原ホテル
  • Year and Date: 2008-11-18
• [Remarks] ホームページ等
  • URL: http://www2.math.kyushu-u.ac.jp/~stakagi/
• [Remarks]
  • URL: http://www2.math.kyushu-u.ac.jp/~stakagi/
• [Remarks]
  • URL: http://www2.math.kyushu-u.ac.jp/^-stakagi/
• [Remarks]
  • URL: http://www2.math.kyushu-u.ac.jp/stakagi/