Betti numbers of holomorphic symplectic quotients via arithmetic Fourier transform

T. Hausel, PNAS 103 (2006) 6120–6124.


Journal Article | Published
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.
Publishing Year
Date Published
2006-04-18
Journal Title
PNAS
Acknowledgement
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.
Volume
103
Issue
16
Page
6120 - 6124
IST-REx-ID

Cite this

Hausel T. Betti numbers of holomorphic symplectic quotients via arithmetic Fourier transform. PNAS. 2006;103(16):6120-6124. doi:10.1073/pnas.0601337103
Hausel, T. (2006). Betti numbers of holomorphic symplectic quotients via arithmetic Fourier transform. PNAS, 103(16), 6120–6124. https://doi.org/10.1073/pnas.0601337103
Hausel, Tamas. “Betti Numbers of Holomorphic Symplectic Quotients via Arithmetic Fourier Transform.” PNAS 103, no. 16 (2006): 6120–24. https://doi.org/10.1073/pnas.0601337103.
T. Hausel, “Betti numbers of holomorphic symplectic quotients via arithmetic Fourier transform,” PNAS, vol. 103, no. 16, pp. 6120–6124, 2006.
Hausel T. 2006. Betti numbers of holomorphic symplectic quotients via arithmetic Fourier transform. PNAS. 103(16), 6120–6124.
Hausel, Tamas. “Betti Numbers of Holomorphic Symplectic Quotients via Arithmetic Fourier Transform.” PNAS, vol. 103, no. 16, National Academy of Sciences, 2006, pp. 6120–24, doi:10.1073/pnas.0601337103.

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