Kirwan surjectivity for quiver varieties

Kevin McGerty, Thomas Nevins

Research output: Contribution to journalArticlepeer-review


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 languageEnglish (US)
Pages (from-to)161-187
Number of pages27
JournalInventiones Mathematicae
Issue number1
StatePublished - Apr 1 2018

ASJC Scopus subject areas

  • Mathematics(all)

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