Classification theory of algebraic varieties and derived categories

• Project/Area Number: 20740022
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: Algebra
• Research Institution: Tokyo Metropolitan University
• Principal Investigator: UEHARA Hokuto Tokyo Metropolitan University, 大学院・理工学研究科, 准教授 (80378546)
• Project Period (FY): 2008 – 2010
• Project Status: Completed (Fiscal Year 2010)
• Budget Amount: ¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000); Fiscal Year 2010: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2009: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2008: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
• Keywords: 導来圏 / トーリック多様体 / 楕円曲面 / Torelli型問題

Research Abstract

I obtain some results on Bridgeland stability, a counterexample of birational Torreli problem, and the existence of certain generators of derived categories of certain varieties (like toric Fano 3-folds and so on).

Research Products

• [Journal Article] A counterexample of the birational Torelli problem via Fourier--Mukai transform (2011)
  • Author(s): 上原北斗
  • Journal Title: J.Algebraic Geom Volume: (Electric version)
  • Peer Reviewed
• [Journal Article] Stability conditions on $A_n$-Singularities (2010)
  • Author(s): Hokuto Uehara, Akira Ishii, Kazushi Ueda
  • Journal Title: J.Differential Geom. 84 Pages: 87-126
  • Peer Reviewed
• [Journal Article] Tilting generators via ample line bundles (2010)
  • Author(s): Hokuto Uehara, Yukinobu Toda
  • Journal Title: Advances in Mathematics. 233 Pages: 1-29
  • Peer Reviewed
• [Journal Article] Stability conditions on $A_n$-singularities (2010)
  • Author(s): Hokuto Uehara , Akira Ishii, Kazushi Ueda
  • Journal Title: J.Differential Geom. 84 Pages: 87-126
  • Peer Reviewed
• [Journal Article] Stability conditions on $A_n$-singularities (2010)
  • Author(s): 上原北斗、石井亮、植田一石
  • Journal Title: J.Differential Geom. 84 Pages: 87-126
  • Peer Reviewed
• [Journal Article] Tilting generators via ample line bundles (2010)
  • Author(s): 上原北斗、戸田幸伸
  • Journal Title: Advances in Mathematics. 233 Pages: 1-29
  • Peer Reviewed
• [Journal Article] Three-dimensional terminal toric flip (2009)
  • Author(s): Hokuto Uehara Osamu Fujino, Hiroshi Sato, Yukishige Takano
  • Journal Title: Cent.Ear.J.Math. 7 Pages: 46-53
  • Peer Reviewed
• [Journal Article] Three-dimensional terminal toric flip (2009)
  • Author(s): Hokuto Uehara, Osamu Fujino, Hiroshi Sato, Yukishige Takano
  • Journal Title: Cent.Eur.J.Math. 7 Pages: 46-53
  • Peer Reviewed
• [Journal Article] Three-dimensional terminal tonic flip (2009)
  • Author(s): 藤野修、佐藤拓、高野有紀篤、上原北斗
  • Journal Title: Cent. Eur. J. Math. 7 Pages: 46-53
  • Peer Reviewed
• [Journal Article] A counterexample of the birational Torelli problem via Fourier-Mukai transform
  • Author(s): Hokuto Uehara
  • Journal Title: J.Algebraic Geom
  • Peer Reviewed
• [Journal Article] A counterexample of the birational Torelli problem via Fourier-Mukai transform
  • Author(s): Hokuto Uehara
  • Journal Title: J.Algebraic Geom (受理済み)
  • Peer Reviewed
• [Presentation] Generators by Frobenius push-forward on smooth toric surfaces (2011)
  • Author(s): 上原北斗
  • Organizer: Workshop on Non commutative Geometryand the McKay Correspondence
  • Place of Presentation: 名占屋大学(招待講演)
  • Year and Date: 2011-03-15
• [Presentation] Generators by Frobenius push-forward on smooth toric surfaces (2011)
  • Author(s): 上原北斗
  • Organizer: Workshop on Non-commutative Geometry and the McKay Correspondence
  • Place of Presentation: 名古屋大学(招待講演)
  • Year and Date: 2011-03-15
• [Presentation] Generators by Frobenius push-forward on smooth toric surfaces (2011)
  • Author(s): 上原北斗
  • Organizer: Workshop on Non-commutative Geometry and the McKay Correspondence
  • Place of Presentation: 名古屋大学
  • Year and Date: 2011-03-15
• [Presentation] Exceptional collectionson toric Fano threefolds and birational geometry (2010)
  • Author(s): 上原北斗
  • Organizer: 代数幾何とホモトピー論の新展開
  • Place of Presentation: 東京都市大学(招待講演)
  • Year and Date: 2010-12-17
• [Presentation] Exceptional collections on toric Fano threefolds and birational geometry (2010)
  • Author(s): 上原北斗
  • Organizer: 代数幾何とホモトピー論の新展開
  • Place of Presentation: 東京都市大学(招待講演)
  • Year and Date: 2010-12-17
• [Presentation] Exceptional collections on toric Fano threefolds and birational geometry (2010)
  • Author(s): 上原北斗
  • Organizer: 代数幾何とホモトピー論の新展開
  • Place of Presentation: 東京都市大学
  • Year and Date: 2010-12-17
• [Presentation] McKay correspondenceand derived categories (2010)
  • Author(s): 上原北斗
  • Organizer: 都の西北代数幾何学シンポジウム
  • Place of Presentation: 早稲田大学(招待講演)
  • Year and Date: 2010-11-11
• [Presentation] McKay correspondence and derived categories (2010)
  • Author(s): 上原北斗
  • Organizer: 都の西北 代数幾何学シンポジウム
  • Place of Presentation: 早稲田大学(招待講演)
  • Year and Date: 2010-11-11
• [Presentation] McKay correspondence and derived categories (2010)
  • Author(s): 上原北斗
  • Organizer: 都の西北 代数幾何学シンポジウム
  • Place of Presentation: 早稲田大学
  • Year and Date: 2010-11-11
• [Presentation] Tilting generators via ampleline bundles (2010)
  • Author(s): 上原北斗
  • Organizer: Summer meeting of the Canadian Mathematical Society
  • Place of Presentation: カナダ, University of New Brunswick(招待講演)
  • Year and Date: 2010-06-07
• [Presentation] Tilting generators via ample line bundles (2010)
  • Author(s): 上原北斗
  • Organizer: Summer meeting of the Canadian Mathematical Society
  • Place of Presentation: カナダ, University of New Brunswick(招待講演)
  • Year and Date: 2010-06-07
• [Presentation] Tilting generators via ample line bundles (2010)
  • Author(s): 上原北斗
  • Organizer: Summer meeting of the Canadian Mathematical Society
  • Place of Presentation: カナダ・フレデリクトン
  • Year and Date: 2010-06-04
• [Presentation] Tilting generators via ample line bundles (2009)
  • Author(s): 上原北斗
  • Organizer: 国際研究集会「Interactions Between Noncommutative Algebra and Algebraic Geometry
  • Place of Presentation: カナダ,バンフ,BIRS(招待講演)
  • Year and Date: 2009-10-29
• [Presentation] Tilting generators via ample line bundles (2009)
  • Author(s): 上原北斗
  • Organizer: 国際研究集会 「Interactions Between Noncommutative Algebra and Algebraic Geometry」
  • Place of Presentation: カナダ, バンフ, BIRS(招待講演)
  • Year and Date: 2009-10-29
• [Presentation] Fourier-Mukai numbers of minimal elliptic rational surfaces (2009)
  • Author(s): 上原北斗
  • Organizer: Summer meeting of the Canadian Mathematical Society
  • Place of Presentation: カナダ・ニューファンドランド
  • Year and Date: 2009-06-07
• [Presentation] Pourier-Mukai numbers of minimal elliptic rational surfaces (2009)
  • Author(s): 上原北斗
  • Organizer: Summer meeting of the Canadian Mathematical Society
  • Place of Presentation: カナダ,Memorial University of Newfoundland(招待講演)
  • Year and Date: 2009-06-05
• [Presentation] Fourier-Mukai numbers of minimal elliptic rational surfaces (2009)
  • Author(s): 上原北斗
  • Organizer: Summer meeting of the Canadian Mathematical Society
  • Place of Presentation: カナダ, Memorial University of Newfoundland(招待講演)
  • Year and Date: 2009-06-05
• [Presentation] Fourier-Mukai numbers of minimal elliptic rational surfaces (2009)
  • Author(s): 上原北斗
  • Organizer: 第4回代数、解析、幾何セミナー
  • Place of Presentation: 鹿児島大学(招待講演)
  • Year and Date: 2009-02-18
• [Presentation] Tilting generators via ample line bundles (2008)
  • Author(s): 上原北斗
  • Organizer: Interactions Between Noncommutative Algebra and Algebraic Geometry
  • Place of Presentation: カナダ・バンフ
  • Year and Date: 2008-10-30
• [Presentation] Tilting generators via ample line bundles (2008)
  • Author(s): 上原北斗
  • Organizer: 国際研究集会「Vector bundles」
  • Place of Presentation: インド,ムンバイ,TATA研究所(招待講演)
  • Year and Date: 2008-03-06
• [Presentation] Tilting generators via ample line bundles (2008)
  • Author(s): 上原北斗
  • Organizer: 国際研究集会 「Vector bundles」
  • Place of Presentation: インド, ムンバイ, TATA研究所(招待講演)
  • Year and Date: 2008-03-06
• [Presentation] Fourier-Mukai numbers of minimal elliptic rational surfaces (2008)
  • Author(s): 上原北斗
  • Organizer: 第4回代数、解析、幾何セミナー
  • Place of Presentation: 鹿児島大学
  • Year and Date: 2008-02-19
• [Remarks] ホームページ等