Abelian and non-Abelian quotient

2014 Fiscal Year Final Research Report

• 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
• Keywords: 局所化定理 / Gromov-Witten不変量 / tautological環

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.

Free Research Field

代数幾何学