Abelian and non-Abelian quotient

• Project/Area Number: 23740039
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Algebra
• Research Institution: Kagawa National College of Technology
• Principal Investigator: SATOU Humitoshi 香川高等専門学校, 一般教育科, 准教授 (20548309)
• Project Period (FY): 2011-04-28 – 2015-03-31
• Project Status: Completed (Fiscal Year 2014)
• Budget Amount: ¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000); Fiscal Year 2014: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2013: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2012: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2011: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
• Keywords: 局所化定理 / Gromov-Witten不変量 / tautological環 / Ａｂｅｌ商 / 非Abel商 / アーベル商 / Gromov-Witten普遍量 / Tautological Ring / orbifold cohomology

Outline of Final Research Achievements

We studied following two things.
One is that we find an explicit relations between orbifold cohomology rings of non-abelian quotient X//G and abelian quotient X//T, where X is a complex manifold with an action by a semi-simple Lie group G and T is its maximal torus. The other one is that we find an algorithm to find two new relation in tautological rings of moduli stack of genus g stable curves by applying Atiyah-Bott localization theorem to a moduli stack of genus g stable maps to a projective line. We also carried out our algorithm to obtain one of two relations in terms of boundary classes explicitly.

Research Products

• [Journal Article] The Chow motives of relative Fulton-MacPherson space (2013)
  • Author(s): Sato, Fumitoshi
  • Journal Title: Mathematica Scandinavica Volume: 113 Pages: 20-29
  • Peer Reviewed
• [Journal Article] The Chow motives of relative Fulton-MacPherson space (2013)
  • Author(s): Fumitoshi Sato
  • Journal Title: Mathematica Scandinavica Volume: N/A
  • Peer Reviewed
• [Presentation] Topological recursion relations via degree two map (2014)
  • Author(s): 佐藤文敏
  • Organizer: 代数幾何学セミナー
  • Place of Presentation: 東北大学
  • Year and Date: 2014-12-05
  • Invited
• [Presentation] Topological recursion relations via degree two map (2014)
  • Author(s): 佐藤文敏
  • Organizer: リーマン面に関連する位相幾何学2014
  • Place of Presentation: 東京大学
  • Year and Date: 2014-08-28
  • Invited
• [Presentation] Topological recursion relations (2013)
  • Author(s): 佐藤 文敏
  • Organizer: 第11回アフィン代数幾何学研究集会
  • Place of Presentation: 関西学院大学大阪梅田キャンパス
  • Invited
• [Presentation] 数え上げ幾何学と微分方程式 (2012)
  • Author(s): 佐藤 文敏
  • Organizer: 第11回山口大学理学部講演会
  • Place of Presentation: 山口大学理学部
  • Invited
• [Presentation] Deformation of a smooth Deligne-Mumford stack via differential graded Lie algebra (2011)
  • Author(s): 佐藤 文敏
  • Organizer: Cox Ring, Motivic Zeta, and Related Topics(招待講演)
  • Place of Presentation: 広島大学
• [Presentation] Enumerative geometry of the moduli of genus 3 curves
  • Author(s): 佐藤文敏
  • Organizer: Branched Coverings, Degenerations, and Related Topics 2014
  • Place of Presentation: 広島大学
  • Invited
• [Presentation] Ｔopological recursion relations
  • Author(s): 佐藤文敏
  • Organizer: リーマン面に関連する位相幾何学
  • Place of Presentation: 東京大学
  • Invited
• [Remarks] 研究教育活動等報告書
  • URL: http://www.kagawa-nct.ac.jp/course/GE/takamatsu/g/fumi/g3854.html