Kirwan surjectivity for quiver varieties

Abstract

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.

References in corpus (2)

• Hyperpolygons and Hitchin systems
• Categorical Cell Decomposition of Quantized Symplectic Algebraic Varieties

Cited by in corpus (12)

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• Characters of tangent spaces at torus fixed points and $3d$-mirror symmetry
• Moduli spaces of generalized hyperpolygons
• Evidence for an Algebra of ${\mathbf{G}}_2$ Instantons
• Affine $\mathcal{W}$-algebras and Miura maps from 3d $\mathcal{N}=4$ non-Abelian quiver gauge theories
• On the Kirwan map for moduli of Higgs bundles
• Framed cohomological Hall algebras and cohomological stable envelopes
• ${\text{AdS}}_4$ Holography and the Hilbert Scheme
• Elliptic Stable Envelopes for Certain Non-Symplectic Varieties and Dynamical $R$-Matrices for Superspin Chains from the Bethe/Gauge Correspondence
• Harish-Chandra bimodules for type A rational Cherednik algebras
• Kirwan surjectivity and Lefschetz-Sommese theorems for a generalized hyperkähler reduction