--- _id: '1473' 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. author: - first_name: Tamas full_name: Tamas Hausel id: 4A0666D8-F248-11E8-B48F-1D18A9856A87 last_name: Hausel - first_name: Fernando full_name: Rodríguez Villegas, Fernando last_name: Rodríguez Villegas citation: ama: Hausel T, Rodríguez Villegas F. Cohomology of large semiprojective hyperkähler varieties. Asterisque. 2015;2015(370):113-156. apa: Hausel, T., & Rodríguez Villegas, F. (2015). Cohomology of large semiprojective hyperkähler varieties. Asterisque. Societe Mathematique de France. chicago: Hausel, Tamás, and Fernando Rodríguez Villegas. “Cohomology of Large Semiprojective Hyperkähler Varieties.” Asterisque. Societe Mathematique de France, 2015. ieee: T. Hausel and F. Rodríguez Villegas, “Cohomology of large semiprojective hyperkähler varieties,” Asterisque, vol. 2015, no. 370. Societe Mathematique de France, pp. 113–156, 2015. ista: Hausel T, Rodríguez Villegas F. 2015. Cohomology of large semiprojective hyperkähler varieties. Asterisque. 2015(370), 113–156. mla: Hausel, Tamás, and Fernando Rodríguez Villegas. “Cohomology of Large Semiprojective Hyperkähler Varieties.” Asterisque, vol. 2015, no. 370, Societe Mathematique de France, 2015, pp. 113–56. short: T. Hausel, F. Rodríguez Villegas, Asterisque 2015 (2015) 113–156. date_created: 2018-12-11T11:52:13Z date_published: 2015-01-01T00:00:00Z date_updated: 2021-01-12T06:50:59Z day: '01' extern: 1 intvolume: ' 2015' issue: '370' main_file_link: - open_access: '1' url: http://arxiv.org/abs/1309.4914 month: '01' oa: 1 page: 113 - 156 publication: Asterisque publication_status: published publisher: Societe Mathematique de France publist_id: '5723' quality_controlled: 0 status: public title: Cohomology of large semiprojective hyperkähler varieties type: review volume: 2015 year: '2015' ...