{"type":"journal_article","doi":"10.1073/pnas.0601337103","page":"6120 - 6124","oa":1,"_id":"1462","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.","publication":"PNAS","publication_status":"published","issue":"16","author":[{"id":"4A0666D8-F248-11E8-B48F-1D18A9856A87","full_name":"Tamas Hausel","last_name":"Hausel","first_name":"Tamas"}],"status":"public","date_created":"2018-12-11T11:52:10Z","abstract":[{"text":"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.","lang":"eng"}],"volume":103,"date_updated":"2021-01-12T06:50:55Z","publist_id":"5734","year":"2006","month":"04","publisher":"National Academy of Sciences","day":"18","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/math/0511163"}],"quality_controlled":0,"title":"Betti numbers of holomorphic symplectic quotients via arithmetic Fourier transform","extern":1,"date_published":"2006-04-18T00:00:00Z","citation":{"ieee":"T. Hausel, “Betti numbers of holomorphic symplectic quotients via arithmetic Fourier transform,” <i>PNAS</i>, vol. 103, no. 16. National Academy of Sciences, pp. 6120–6124, 2006.","ama":"Hausel T. Betti numbers of holomorphic symplectic quotients via arithmetic Fourier transform. <i>PNAS</i>. 2006;103(16):6120-6124. doi:<a href=\"https://doi.org/10.1073/pnas.0601337103\">10.1073/pnas.0601337103</a>","short":"T. Hausel, PNAS 103 (2006) 6120–6124.","mla":"Hausel, Tamás. “Betti Numbers of Holomorphic Symplectic Quotients via Arithmetic Fourier Transform.” <i>PNAS</i>, vol. 103, no. 16, National Academy of Sciences, 2006, pp. 6120–24, doi:<a href=\"https://doi.org/10.1073/pnas.0601337103\">10.1073/pnas.0601337103</a>.","ista":"Hausel T. 2006. Betti numbers of holomorphic symplectic quotients via arithmetic Fourier transform. PNAS. 103(16), 6120–6124.","apa":"Hausel, T. (2006). Betti numbers of holomorphic symplectic quotients via arithmetic Fourier transform. <i>PNAS</i>. National Academy of Sciences. <a href=\"https://doi.org/10.1073/pnas.0601337103\">https://doi.org/10.1073/pnas.0601337103</a>","chicago":"Hausel, Tamás. “Betti Numbers of Holomorphic Symplectic Quotients via Arithmetic Fourier Transform.” <i>PNAS</i>. National Academy of Sciences, 2006. <a href=\"https://doi.org/10.1073/pnas.0601337103\">https://doi.org/10.1073/pnas.0601337103</a>."},"intvolume":"       103"}