Betti numbers of holomorphic symplectic quotients via arithmetic Fourier transform

Abstract

A Fourier transform technique is introduced for counting the number of solutions of holomorphic moment map equations over a finite field. This in turn gives information on Betti numbers of holomorphic symplectic quotients. As a consequence simple unified proofs are obtained for formulas of Poincare polynomials of toric hyperkahler varieties, Poincare polynomials of Hilbert schemes of points and twisted ADHM spaces of instantons on C^2 and Poincare polynomials of all Nakajima quiver varieties. As an application, a proof of a conjecture of Kac on the number of absolutely indecomposable representations of a quiver is announced.

8 pages, references and an announcement of a proof of a conjecture of Kac are added

Cited by in corpus (18)

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• A Superconformal Index for HyperKähler Cones
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• S-duality in hyperkaehler Hodge theory
• Kac's conjecture from Nakajima quiver varieties
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• Motivic classes of Nakajima quiver varieties
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