{"author":[{"last_name":"Hausel","id":"4A0666D8-F248-11E8-B48F-1D18A9856A87","first_name":"Tamas","full_name":"Tamas Hausel"},{"full_name":"Rodríguez Villegas, Fernando","last_name":"Rodríguez Villegas","first_name":"Fernando"}],"year":"2015","abstract":[{"lang":"eng","text":"In this paper we survey geometric and arithmetic techniques to study the cohomology of semiprojective hyperkähler manifolds including toric hyperkähler varieties, Nakajima quiver varieties and moduli spaces of Higgs bundles on Riemann surfaces. The resulting formulae for their Poincaré polynomials are combinatorial and representation theoretical in nature. In particular we will look at their Betti numbers and will establish some results and state some expectations on their asymptotic shape."}],"issue":"370","page":"113 - 156","oa":1,"type":"review","month":"01","publisher":"Societe Mathematique de France","publist_id":"5723","date_created":"2018-12-11T11:52:13Z","title":"Cohomology of large semiprojective hyperkähler varieties","quality_controlled":0,"citation":{"ama":"Hausel T, Rodríguez Villegas F. Cohomology of large semiprojective hyperkähler varieties. <i>Asterisque</i>. 2015;2015(370):113-156.","ieee":"T. Hausel and F. Rodríguez Villegas, “Cohomology of large semiprojective hyperkähler varieties,” <i>Asterisque</i>, vol. 2015, no. 370. Societe Mathematique de France, pp. 113–156, 2015.","mla":"Hausel, Tamás, and Fernando Rodríguez Villegas. “Cohomology of Large Semiprojective Hyperkähler Varieties.” <i>Asterisque</i>, vol. 2015, no. 370, Societe Mathematique de France, 2015, pp. 113–56.","short":"T. Hausel, F. Rodríguez Villegas, Asterisque 2015 (2015) 113–156.","ista":"Hausel T, Rodríguez Villegas F. 2015. Cohomology of large semiprojective hyperkähler varieties. Asterisque. 2015(370), 113–156.","apa":"Hausel, T., &#38; Rodríguez Villegas, F. (2015). Cohomology of large semiprojective hyperkähler varieties. <i>Asterisque</i>. Societe Mathematique de France.","chicago":"Hausel, Tamás, and Fernando Rodríguez Villegas. “Cohomology of Large Semiprojective Hyperkähler Varieties.” <i>Asterisque</i>. Societe Mathematique de France, 2015."},"intvolume":"      2015","date_published":"2015-01-01T00:00:00Z","date_updated":"2021-01-12T06:50:59Z","status":"public","extern":1,"day":"01","publication_status":"published","volume":2015,"_id":"1473","publication":"Asterisque","main_file_link":[{"url":"http://arxiv.org/abs/1309.4914","open_access":"1"}]}