Characteristic classes of algebraic stacks and application to enumerative problems

2015 Fiscal Year Final Research Report

• Project/Area Number: 24340007
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Partial Multi-year Fund
• Section: 一般
• Research Field: Geometry
• Research Institution: Hokkaido University
• Principal Investigator: Ohmoto Toru 北海道大学, 理学(系)研究科(研究院), 教授 (20264400)
• Co-Investigator(Kenkyū-buntansha): NARUSE Hiroshi 山梨大学, 総合研究部, 教授 (20172596) ; SUWA Tatsuo 北海道大学, 名誉教授 (40109418) ; YOKURA Shoji 鹿児島大学, 学術研究院理工学域理学系, 教授 (60182680)
• Project Period (FY): 2012-04-01 – 2016-03-31
• Keywords: 特異点論 / 特性類理論 / チャーン類 / トム多項式 / 数え上げ幾何

Outline of Final Research Achievements

Seeking for the complete foundation of the enumerative theory of singularities of maps, I have developed singular Chern class theory on various moduli spaces; in particular, together with collaborators I completed a sequence of works on zeta functions of homology characteristic classes of Hilbert schemes of points on a non-singular variety; I applied the theory of equivariant singular Chern classes to the classification theory of map-germs, that made a new breakthrough for computing singular Milnor numbers.

Free Research Field

特異点論