Studies of varieties of Fano type

• Project/Area Number: 24840009
• Research Category: Grant-in-Aid for Research Activity Start-up
• Allocation Type: Single-year Grants
• Research Field: Algebra
• Research Institution: The University of Tokyo
• Principal Investigator: GONGYO Yoshinori 東京大学, 数理(科)学研究科(研究院), 助教 (70634210)
• Project Period (FY): 2012-08-31 – 2014-03-31
• Project Status: Completed (Fiscal Year 2013)
• Budget Amount: ¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000); Fiscal Year 2013: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000); Fiscal Year 2012: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
• Keywords: 対数的ファノ多様体 / 大域的F正則多様体 / 正標数上のMMP / ファノ多様体 / 正標数還元 / カラビ・ヤウ多様体 / 大域的F分解多様体

Research Abstract

In our studies of varieties of Fano type, during the term when I received this grant, I obtains the following results: characterization vis anti-canonical ring (joint work with Paolo Cascini), rational chain connectedness of globally F-regular threefold, which is theF-singularity theoretical object corresponding to Fano type variety in characteristics lager than and equal 11 (joint work with Zhiyuan Li, Zsolt Patakfalvi, Karl Schwede, Hiromu Tanaka, Hong R. Zong), log Calabi--Yau-ness of surface of globally F-split type(joint work with Shusuke Takagi), and uniform bounds about characteristis for strongly F-regular surfaces (joint work with Paolo Cascini, Karl Schwede).

Research Products

• [Journal Article] Log pluricanonical representations and the abundance conjecture (2014)
  • Author(s): Osamu Fujino, and Yoshinori Gongyo
  • Journal Title: Compositio Math Volume: 150, No.4 Pages: 593-620
• [Journal Article] On log canonical rings (2013)
  • Author(s): Osamu Fujino, and Yoshinori Gongyo
  • Journal Title: Kawamata 60 proceedings Volume: (preprint, to appear)
• [Journal Article] On the anti-canonical ring and varieties of Fano type (2013)
  • Author(s): Paolo Cascini, and Yoshinori Gongyo
  • Journal Title: Saitama Math. J Volume: Vol.30 Pages: 27-38
• [Journal Article] On the anti-canonical ring and varieties of Fano type (2013)
  • Author(s): Paolo Cascini, Yoshinori Gongyo
  • Journal Title: Saitama Math. J. Volume: 30
  • Peer Reviewed
• [Journal Article] Abundance theorem for numerically trivial log canonical divisors of semi-log canonical pairs (2013)
  • Author(s): Yoshinori Gongyo
  • Journal Title: J. Algebraic Geom. Volume: 22 Issue: 3 Pages: 549-564
  • DOI: 10.1090/s1056-3911-2012-00593-1
  • Peer Reviewed
• [Journal Article] Reduction maps and minimal model theory (2012)
  • Author(s): Yoshinori Gongyo and Brian Lehmann
  • Journal Title: Compositio Math. Volume: 149, No.2 Issue: 2 Pages: 295-308
  • DOI: 10.1112/s0010437x12000553
  • Peer Reviewed
• [Journal Article] Characterizaton of varieties of Fano type via singularities of Cox rings
  • Author(s): Yoshinori Gongyo, Shinnosuke Okawa, Akiyoshi Sannai, and Shunsuke Takagi
  • Journal Title: J. Algebraic Geom Volume: (to appear)
• [Journal Article] On images of weak Fano manifolds II
  • Author(s): Osamu Fujino, and Yoshinori Gongyo
  • Journal Title: Proceedings of the conference Algebraic and Complex Geometry in honor of Professor Hulek's sixtieth birthday- Volume: (to appear)
• [Journal Article] On the moduli ivisors of lc-trivial fibrations
  • Author(s): Osamu Fujino, and Yoshinori Gongyo
  • Journal Title: Ann. Inst. Fourier Volume: (to appear)
• [Presentation] On log canonical rings (2014)
  • Author(s): Yoshinori Gongyo
  • Organizer: 第26回可換環セミナー
  • Place of Presentation: 北海道
  • Invited
• [Presentation] On characterizations of log Fano varieties (2013)
  • Organizer: 埼玉大学代数幾何セミナー
  • Year and Date: 2013-10-30
• [Presentation] On the moduli b-divisors of lc-trivial fibrations (2013)
  • Organizer: Workshop on birational geometry
  • Place of Presentation: the University of Tokyo
  • Year and Date: 2013-01-18
• [Presentation] "One approach to the abundance conjecture" & "Finiteness of log pluri-canonical representations" (2013)
  • Organizer: KAIST
  • Place of Presentation: Korea
• [Presentation] On characterizations of log Fano varieties (2013)
  • Organizer: Classification of Algebraic Varieties and related topics
  • Place of Presentation: Cetraro, Italy
• [Presentation] On varieties of Fano type and anti-canonical rings (2013)
  • Organizer: Conference on Moduli and Birational Geometry IV
  • Place of Presentation: POSTECH, Korea
• [Presentation] Surface of globally F-split type (2013)
  • Organizer: Complex Geometry
  • Place of Presentation: IMS, Singapore
• [Presentation] Finiteness of log pluricanonical representations (2013)
  • Organizer: Workshop on Algebaraic Geometry, Edge days
  • Place of Presentation: Edinburgh, UK.
• [Presentation] Characterization of varieties of Fano type via singularities of Cox rings (2013)
  • Organizer: Mathematisches Forschungsinstitut Oberwolfach
  • Place of Presentation: Germany, Complex Algebraic Geometry
• [Presentation] Surface of globally F-split type (2013)
  • Organizer: Workshop in Algebraic Geometry London
  • Place of Presentation: Imperial College London, UK.
• [Presentation] On varieties of globally F-regular and F-split type (2013)
  • Organizer: Workshop : Characteristic p methods in Algebraic Geometry, London
  • Place of Presentation: Imperial College London, UK.
• [Presentation] Characterization of varieties of Fano type via singularities of Cox rings (2013)
  • Organizer: Higher Dimensional Algebraic Geometry
  • Place of Presentation: National Taiwan University, 台北, 台湾
• [Presentation] On characterizations of log Fano varieties (2013)
  • Author(s): Yoshinori Gongyo
  • Organizer: 埼玉大学代数幾何セミナー
  • Place of Presentation: 埼玉大学
  • Invited
• [Presentation] On characterizations of log Fano varieties (2013)
  • Author(s): Yoshinori Gongyo
  • Organizer: Classification of Algebraic Varieties and related topics
  • Place of Presentation: Cetraro
  • Invited
• [Presentation] Finiteness of log pluricanonical representations (2013)
  • Author(s): Yoshinori Gongyo
  • Organizer: Workshop on Algebaraic Geometry, Edge days
  • Place of Presentation: Edinburgh
  • Invited
• [Presentation] Characterization of varieties of Fano type via singularities of Cox rings (2013)
  • Author(s): Yoshinori Gongyo
  • Organizer: Complex Algebraic Geometry
  • Place of Presentation: Mathematisches Forschungsinstitut Oberwolfach, Germany
  • Invited
• [Presentation] Surface of globally F-split type (2013)
  • Author(s): Yoshinori Gongyo
  • Organizer: Workshop in Algebraic Geometry London
  • Place of Presentation: Imperial College London
  • Invited
• [Presentation] On varieties of globally F-regular and F-split type (2013)
  • Author(s): Yoshinori Gongyo
  • Organizer: Workshop: Characteristic p methods in Algebraic Geometry,
  • Place of Presentation: Imperial College London
  • Invited
• [Presentation] Characterization of varieties of Fano type via singularities of Cox rings (2013)
  • Author(s): Yoshinori Gongyo
  • Organizer: Higher Dimensional Algebraic Geometry
  • Place of Presentation: 台湾国立大学
  • Invited
• [Presentation] On varieties of globally F-regular and F-split type (2013)
  • Author(s): Yoshinori Gongyo
  • Organizer: Workshop: Characteristic p methods in Algebraic Geometry
  • Place of Presentation: Imperial College London
  • Invited
• [Presentation] Surface of F-split type (2013)
  • Author(s): Yoshinori Gongyo
  • Organizer: Workshop in Algebraic Geometry London
  • Place of Presentation: Imperial College London
  • Invited
• [Presentation] On varieties of globally F-regular type (2012)
  • Organizer: Cambridge Algebraic Geometry Seminer
  • Year and Date: 2012-11-28
• [Presentation] On the moduli b-divisors of lc-trivial fibrations (2012)
  • Organizer: 東京大学代数幾何セミナー
  • Year and Date: 2012-10-15
• [Presentation] Characterization of varieties of Fano type via singularities of Cox rings (2012)
  • Organizer: Joint Seminar in Algebraic and Complex Geometry Freiburg-Nancy-Strasbourg
  • Place of Presentation: Strasbourg, France
  • Year and Date: 2012-10-08
• [Presentation] Finiteness of log pluricanonical representations (2012)
  • Organizer: workshop on the abundance conjecture
  • Place of Presentation: Toulouse, France
  • Year and Date: 2012-10-02
• [Presentation] Remarks on the non-vanishing conjecture (2012)
  • Organizer: 日大特異点セミナー
  • Place of Presentation: 日大
  • Year and Date: 2012-09-24
• [Presentation] 対数的多重標準表現とアバンダンス (2012)
  • Organizer: 日本数学会2012年度秋季代数学分科会特別講演
  • Place of Presentation: 九州大学
  • Year and Date: 2012-09-21
• [Presentation] The abundance conjecture for slc pairs and its applications (2012)
  • Organizer: Mathematisches Forschungsinstitut Oberwolfach
  • Place of Presentation: Germany, Komplexe Analysis
  • Year and Date: 2012-09-06
• [Presentation] Log pluricanonical representations and abundance conjeceture (2012)
  • Organizer: POSTECH Algebraic Geometry Seminar
  • Year and Date: 2012-05-04
• [Presentation] Remarks on the non-vanishing conjecture (2012)
  • Organizer: Korea-Japan Joint Conference in Algebraic Geometry
  • Place of Presentation: Gunsan
• [Presentation] Characterization of varieties of Fano type via singularities of Cox rings (2012)
  • Organizer: Workshop on Moduli and Birational Geometry
  • Place of Presentation: Busan
• [Presentation] On varieties of globally F-regular type (2012)
  • Organizer: 高次元双有理幾何の周辺
  • Place of Presentation: RIMS
• [Presentation] Characterization of varieties of Fano type via singularities of Cox rings (2012)
  • Author(s): Yoshinori Gongyo
  • Organizer: Joint Seminar in Algebraic and Complex Geometry Freiburg-Nancy-Strasbourg
  • Place of Presentation: Strasbourg
  • Invited
• [Presentation] On varieties of globally F-regular type (2012)
  • Author(s): Yoshinori Gongyo
  • Organizer: Cambridge Algebraic Geometry Seminar
  • Place of Presentation: Cambridge
  • Invited
• [Remarks]
  • URL: http://www.ms.u-tokyo.ac.jp/~gongy
• [Remarks] Yoshinor Gongyo's webpage
  • URL: http://www.ms.u-tokyo.ac.jp/~gongyo
• [Remarks] Y. Gongyo's webpage
  • URL: http://www.ms.u-tokyo.ac.jp/~gongyo/