{"doi":"10.1073/pnas.0601337103","type":"journal_article","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,"citation":{"ista":"Hausel T. 2006. Betti numbers of holomorphic symplectic quotients via arithmetic Fourier transform. PNAS. 103(16), 6120–6124.","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>","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.","short":"T. Hausel, PNAS 103 (2006) 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>.","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>."},"main_file_link":[{"url":"http://arxiv.org/abs/math/0511163","open_access":"1"}],"day":"18","date_published":"2006-04-18T00:00:00Z","month":"04","_id":"1462","oa":1,"publist_id":"5734","publication":"PNAS","publisher":"National Academy of Sciences","intvolume":"       103","publication_status":"published","author":[{"first_name":"Tamas","id":"4A0666D8-F248-11E8-B48F-1D18A9856A87","full_name":"Tamas Hausel","last_name":"Hausel"}],"date_created":"2018-12-11T11:52:10Z","date_updated":"2021-01-12T06:50:55Z","status":"public","page":"6120 - 6124","extern":1,"quality_controlled":0,"year":"2006","issue":"16","title":"Betti numbers of holomorphic symplectic quotients via arithmetic Fourier transform","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"}]}