27. Hausel, T.: Betti numbers of holomorphic symplectic quotients via arithmetic Fourier transform, arxiv:math.AG/0511163
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 Poincaré polynomials of toric hyperkähler varieties (recovering results of Bielawski-Dancer and Hausel-Sturmfels), Poincaré polynomials of Hilbert schemes of points and twisted ADHM spaces of instantons on C^2 (recovering results of Nakajima-Yoshioka) and Poincaré polynomials of all Nakajima quiver varieties.