Hyperbolicity of the Space of Stability Conditions

• Project/Area Number: 25800010
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Algebra
• Research Institution: Nagoya University
• Principal Investigator: Kawatani Kotaro 名古屋大学, 多元数理科学研究科, 博士研究員 (90622150)
• Project Period (FY): 2013-04-01 – 2016-03-31
• Project Status: Completed (Fiscal Year 2015)
• Budget Amount: ¥2,860,000 (Direct Cost: ¥2,200,000、Indirect Cost: ¥660,000); Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2014: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000); Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
• Keywords: 連接層の導来圏 / 安定性条件の空間 / 純層 / 有理二重特異点 / 導来圏 / クライン特異点 / 無限次元Lie環

Outline of Final Research Achievements

The main results of these program is "the classification" of pure sheaves on type D singular points. More precisely, we show that it is impossible to classify pure sheaves on type D singular points. We have to remark that

Research Products

• [Journal Article] Fourier-Mukai transformations on K3 surfaces with rho =1 and Atkin-Lehner involutions (2014)
  • Author(s): Kotaro Kawatani
  • Journal Title: Journal of Algebra Volume: 417 Pages: 103-115
  • DOI: 10.1016/j.jalgebra.2014.06.022
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Presentation] Stability conditions and Fourier-Mukai transformations on K3 surfaces with rho=1 (2014)
  • Author(s): Kotaro Kawatani
  • Organizer: 代数幾何城崎シンポジウム
  • Place of Presentation: 城崎国際アートセンター
  • Year and Date: 2014-10-20 – 2014-10-24
  • Invited
• [Presentation] Stability conditions and Fourier-Mukai transformations on K3 surfaces K3 surfaces with rho=1 (2014)
  • Author(s): 川谷康太郎
  • Organizer: 第8回秋葉原代数曲面ワークショップ
  • Place of Presentation: 首都大学東京 秋葉原サテライトキャンパス
  • Year and Date: 2014-10-11
  • Invited
• [Presentation] K3曲面上の安定性条件とFourier-Mukai変換 (2014)
  • Author(s): 川谷康太郎
  • Organizer: 東北大学代数幾何セミナー
  • Place of Presentation: 東北大学
  • Year and Date: 2014-05-09
  • Invited
• [Presentation] Fourier-Mukai亜群とAtkin-Lehner群 (2013)
  • Author(s): 川谷康太郎
  • Organizer: Hodge理論と代数幾何
  • Place of Presentation: 東京電機大学（北千住キャンパス）
  • Invited
• [Presentation] A hyperbolic metric and stability conditions on K3 with ρ=1 (2013)
  • Author(s): 川谷康太郎
  • Organizer: 5th Algebraic Geometry in East Asia
  • Place of Presentation: Mornigside Center of Mathematics Chinese Academy of Sciense
  • Invited