Betti numbers of holomorphic symplectic quotients via arithmetic Fourier transform Journal Article


Author(s): Hausel, Tamás
Article Title: Betti numbers of holomorphic symplectic quotients via arithmetic Fourier transform
Affiliation
Abstract: A Fourier transform technique is introduced for counting the number of solutions of holomorphic moment map equations over a finite field. This technique 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 Hubert schemes of points and twisted Atiyah-Drinfeld-Hitchin-Manin (ADHM) spaces of instantons on ℂ2 (recovering results of Nakajima-Yoshioka), and Poincaré 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.
Keywords: Quiver varieties; Weyl-Kac character formula
Journal Title: PNAS
Volume: 103
Issue 16
ISSN: 1091-6490
Publisher: National Academy of Sciences  
Date Published: 2006-04-18
Start Page: 6120
End Page: 6124
Sponsor: This work was supported by a Royal Society University Research Fellowship, National Science Foundation Grant DMS-0305505, an Alfred P. Sloan Research Fellowship, and a Summer Research Assignment of the University of Texas at Austin.
URL:
DOI: 10.1073/pnas.0601337103
Open access: yes (repository)
IST Austria Authors
  1. Tamás Hausel
    31 Hausel