Kirwan surjectivity for quiver varieties

Kirwan surjectivity for quiver varieties 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Inventiones mathematicae Springer Journals

Kirwan surjectivity for quiver varieties

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Publisher
Springer Journals
Copyright
Copyright © 2017 by Springer-Verlag GmbH Germany
Subject
Mathematics; Mathematics, general
ISSN
0020-9910
eISSN
1432-1297
D.O.I.
10.1007/s00222-017-0765-x
Publisher site
See Article on Publisher Site

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.

Journal

Inventiones mathematicaeSpringer Journals

Published: Nov 9, 2017

References

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