Intersection theory via localization

• Project/Area Number: 21840056
• Research Category: Grant-in-Aid for Research Activity Start-up
• Allocation Type: Single-year Grants
• Research Field: Algebra
• Research Institution: 香川高等専門学校
• Principal Investigator: SATOU Humitoshi 香川高等専門学校, 一般教育科, 講師 (20548309)
• Project Period (FY): 2009 – 2010
• Project Status: Completed (Fiscal Year 2010)
• Budget Amount: ¥2,379,000 (Direct Cost: ¥1,830,000、Indirect Cost: ¥549,000); Fiscal Year 2010: ¥1,248,000 (Direct Cost: ¥960,000、Indirect Cost: ¥288,000); Fiscal Year 2009: ¥1,131,000 (Direct Cost: ¥870,000、Indirect Cost: ¥261,000)
• Keywords: 局所化定理 / Gromov-Witten不変量 / Fulton-MacPherson空間 / 曲線のモジュライ

Research Abstract

We found new recursive formulas of intersections between lambda and psi classes, which generalized formulas in a paper "Towards an enumerative geometry of the moduli space of curves" by David Munford via applying the localization theorem to the graph space of a moduli of point stable curves. We also generalized Fulton-MacPherson configuration space to relative one and compute its Chow motive.

Research Products

• [Journal Article] A generalization of Fulton-MacPherson configuration spaces (2009)
  • Author(s): Kim Bumsig; Sato Fumitoshi
  • Journal Title: Selecta Mathematica (N.S.) 15 no.3 Pages: 435-443
• [Journal Article] Recrusive formula for ψ^g-λ_1ψ^{g-1}+・・・+λ_g in M_{g,1} (2009)
  • Author(s): Arcara Daniele; Sato Fumitoshi
  • Journal Title: Proceedings of American Mathematical Society 137 no.12 Pages: 4077-4081
• [Journal Article] A generalization of Fulton-MacPherson configuration spaces (2009)
  • Author(s): Bumsig Kim
  • Journal Title: Selecta Mathematica, New Series 15 Pages: 435-443
  • Peer Reviewed
• [Journal Article] Recursive Formula for ψ^g-λ_1ψ^(g-1)+…+(-1)^gλg in Mg,_1 (2009)
  • Author(s): Fumitoshi Sato
  • Journal Title: Proceedings of the American Mathematical Society 137 Pages: 4077-4081
  • Peer Reviewed
• [Presentation] A generalization of Fulton-MacPherson spaces (2010)
  • Author(s): 佐藤文敏
  • Organizer: 代数幾何の関連する諸分野
  • Place of Presentation: 北海道大学
  • Year and Date: 2010-08-30
• [Presentation] Enumerative geometry of moduli of curves and Gromov-Witten invariants (2009)
  • Author(s): 佐藤文敏
  • Organizer: Workshop on Schubert Calculus
  • Place of Presentation: 倉敷シーサイドホテル
  • Year and Date: 2009-09-23
• [Remarks] ホームページ等
  • URL: http://www.kagawa-nct.ac.jp/prospectus/publication/kouhou.html
• [Remarks]
  • URL: http://www.kagawa-nct.ac.jp/prospectus/publication/kouhou.html