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Kirwan surjectivity for quiver varieties

Abstract:
For algebraic varieties defined by hyperk¨ahler or, more generally, algebraic symplectic reduction, it is a long-standing question whether the “hyperk¨ahler 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.
Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1007/s00222-017-0765-x

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Oxford college:
Christ Church
Role:
Author
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Funding agency for:
McGerty, K
Grant:
EI/I033343/1
Publisher:
Springer Berlin Heidelberg Publisher's website
Journal:
Inventiones Mathematicae Journal website
Volume:
212
Issue:
1
Pages:
161–187
Publication date:
2017-11-09
Acceptance date:
2017-10-05
DOI:
EISSN:
1432-1297
ISSN:
0020-9910
Source identifiers:
738185
Pubs id:
pubs:738185
UUID:
uuid:88e82ce4-20b4-419c-8672-7e5316fe0db9
Local pid:
pubs:738185
Deposit date:
2017-10-27

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