Various problems related to the classification in higher dimensional birational geometry

2010 Fiscal Year Self-evaluation Report

• Project/Area Number: 20340005
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Algebra
• Research Institution: Kyoto University
• Principal Investigator: MORI Shigefumi Kyoto University, 数理解析研究所, 教授 (00093328)
• Project Period (FY): 2008 – 2012
• Keywords: 端収縮射 / フリップ収縮射 / 因子収縮射 / Qコニック束 / Qデルペゾ束 / 端末特異点 / デュバル特異点 / 一般象予想

Research Abstract

高次元双有理幾何における種々の分類問題を研究する。
特に森は、前科研費において得られたIskovskikh予想の解決をさらに発展させて、3次元において、
(1)Qコニック束の底曲面の非特異点上の構造、
(2)可約なフリップ、
(3)(因子を曲線につぶす)因子収縮射の分類を目的とする。
また、松木は川ノ上と共に正標数の特異点解消の完全解決のため、アルゴリズムの定式化を目指す。

Research Products

• [Journal Article] Threefold extremal contractions of type (IA) (2011)
  • Author(s): Shigefumi Mori, Yuri Prokhorov
  • Journal Title: Kyoto J.Math. 51(2)掲載確定
  • Peer Reviewed
• [Journal Article] Multiple fibers of del Pezzo fibrations (2009)
  • Author(s): S.Mori, Y.Prokhorov
  • Journal Title: Proceedings of the Steklov Institute of Mathematics 264 Pages: 131-145
  • Peer Reviewed
• [Journal Article] On Q-conic bundles, III (2009)
  • Author(s): S.Mori, Y.Prokhorov
  • Journal Title: Publ.RIMS Kyoto Univ. 45 Pages: 787-810
  • Peer Reviewed
• [Journal Article] On Q-conic bundles, II (2008)
  • Author(s): S.Mori, Y.Prokhorov
  • Journal Title: Publ.RIMS Kyoto Univ. 44 Pages: 955-971
  • Peer Reviewed
• [Journal Article] On Q-conic bundles (2008)
  • Author(s): S.Mori, Y.Prokhorov
  • Journal Title: Publ.RIMS Kyoto Univ. 44 Pages: 315-369
  • Peer Reviewed
• [Presentation] Three dimensional Q-conic bundles and related topics (joint work with Y.Prokhorov) (2010)
  • Author(s): 森重文
  • Organizer: International conference "Birational Geometry"
  • Place of Presentation: ICMS (Edinburgh, UK)
  • Year and Date: 2010-12-08
• [Presentation] Three dimensional Q-conic bundles and related topics (joint work with Y.Prokhorov) (2010)
  • Author(s): 森重文
  • Organizer: International workshop "Workshop on Moduli and Birational, Geometry"
  • Place of Presentation: Pohang University of Science and Technology (POSTECH), Korea
  • Year and Date: 2010-08-05
• [Presentation] Three dimensional Q-conic bundles and related topics (joint work with Y.Prokhorov) (2010)
  • Author(s): 森重文
  • Organizer: Mini-Workshop on MMP and RC
  • Place of Presentation: Princeton University
  • Year and Date: 2010-05-21
• [Presentation] On Q-conic bundles (2009)
  • Author(s): 森重文
  • Organizer: International conference "Geometry of Algebraic Varieties" dedicated to the memory of Vasily Alexeevich Iskovskikh
  • Place of Presentation: Steklov Mathematical Institute, Moscow
  • Year and Date: 2009-06-29
• [Presentation] Q-conic bundles and the General Elephant Conjecture. (2008)
  • Author(s): 森重文
  • Organizer: IAS/Park City数学研究所(PCMI)夏期学校
  • Place of Presentation: 米国ユタ州パークシティ
  • Year and Date: 2008-07-24
• [Presentation] Q-conic bundles and the General Elephant Conjecture (2008)
  • Author(s): 森重文
  • Organizer: 60Miles conference
  • Place of Presentation: 連合王国ロンドンUniversity of College London
  • Year and Date: 2008-07-16