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Betti numbers of holomorphic symplectic quotients via arithmetic Fourier transform

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 نشر من قبل Tamas Hausel
 تاريخ النشر 2005
  مجال البحث
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 تأليف Tamas Hausel




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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.



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