Kirwan surjectivity for quiver varieties

Kevin McGerty; Thomas Nevins

doi:10.1007/s00222-017-0765-x

Kirwan surjectivity for quiver varieties

Kevin McGerty, Thomas Nevins

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

For algebraic varieties defined by hyperkähler or, more generally, algebraic symplectic reduction, it is a long-standing question whether the “hyperkähler 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.

Original language	English (US)
Pages (from-to)	161-187
Number of pages	27
Journal	Inventiones Mathematicae
Volume	212
Issue number	1
DOIs	https://doi.org/10.1007/s00222-017-0765-x
State	Published - Apr 1 2018

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abstract = "For algebraic varieties defined by hyperk{\"a}hler or, more generally, algebraic symplectic reduction, it is a long-standing question whether the “hyperk{\"a}hler 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.",

author = "Kevin McGerty and Thomas Nevins",

note = "Funding Information: Acknowledgements We thank G. Bellamy for comments on a draft. Kevin McGerty was supported by EPSRC Programme Grant EI/I033343/1. Thomas Nevins was supported by NSF Grants DMS-1159468 and DMS-1502125. Publisher Copyright: {\textcopyright} 2017, Springer-Verlag GmbH Germany.",

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N2 - For algebraic varieties defined by hyperkähler or, more generally, algebraic symplectic reduction, it is a long-standing question whether the “hyperkähler 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.

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Kirwan surjectivity for quiver varieties

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