---
_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'
...