Residue theory on singular varieties and its applications

2016 Fiscal Year Final Research Report

• Project/Area Number: 24540060
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Geometry
• Research Institution: Hokkaido University
• Principal Investigator: SUWA Tatsuo 北海道大学, ー, 名誉教授 (40109418)
• Co-Investigator(Renkei-kenkyūsha): ASUKE Taro 東京大学, 数理科学研究科, 准教授 (30294515) ; OHMOTO Toru 北海道大学, 理学研究院, 教授 (20264400) ; OKA Mutsuo 東京理科大学, 理学部, 嘱託教授 (40011697) ; TAKEUCHI Kiyoshi 筑波大学, 数理物質科学研究科, 教授 (70281160) ; TAJIMA Shinichi 筑波大学, 数理物質科学研究科, 教授 (70155076) ; NAKAMURA Yayoi 近畿大学, 理工学部, 講師 (60388494) ; YOKURA Shoji 鹿児島大学, 理学部, 教授 (60182680)
• Project Period (FY): 2012-04-01 – 2017-03-31
• Keywords: 幾何学 / 複素解析幾何学 / 特性類の局所化 / 相対コホモロジー / Alexander 双対性 / 留数 / 特異多様体 / 特異葉層構造

Outline of Final Research Achievements

The localization theory of characteristic classes developed by the principal investigator turned out to be very effective in a wide range of problems related to characteristic classes mainly in complex analytic geometry. During the period, we obtained the following results.
(1) As to the degeneracy loci problem of vector bundle homomorphisms, we constructed a universal localization. (2) We generalized the Lefschetz coincidence point formula. For this, the local and global homology classes we introduced played key roles. (3) We developed the theory of relative Bott-Chen cohomology and give some applications. (4) We discovered a simple way of expressing Sato hyperfunctions. For this we strengthened the theory of relative Dolbeault cohomology. We also gave simple expressions of fundamental operations on the hyperfunctions.

Free Research Field

複素解析幾何学