Kirwan surjectivity for quiver varieties

• 成果类型: Article
• 署名作者: McGerty, Kevin; Nevins, Thomas
• 署名单位: University of Oxford; University of Illinois System; University of Illinois Urbana-Champaign
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-017-0765-x
• 发表日期: 2018
• 页码: 161-187
• 关键词: cohomology ring; REPRESENTATIONS; ALGEBRAS; MODULES

摘要

For algebraic varieties defined by hyperkahler or, more generally, algebraic symplectic reduction, it is a long-standing question whether the hyperkahler Kirwan map on cohomology is surjective. We resolve this question in the affirmative for Nakajima quiver varieties. We also establish similar results for other cohomology theories and for the derived category. Our proofs use only classical topological and geometric arguments.