Cohomology of large semiprojective hyperkaehler varieties

Abstract

In this paper we survey geometric and arithmetic techniques to study the cohomology of semiprojective hyperkaehler manifolds including toric hyperkaehler varieties, Nakajima quiver varieties and moduli spaces of Higgs bundles on Riemann surfaces. The resulting formulae for their Poincare polynomials are combinatorial and representation theoretical in nature. In particular we will look at their Betti numbers and will establish some results and expectations on their asymptotic shape.

43 pages, 11 figures

References in corpus (1)

• Topology of Hitchin systems and Hodge theory of character varieties: the case A_1

Cited by in corpus (5)

• Hyperpolygons and Hitchin systems
• Aspects of the topology and combinatorics of Higgs bundle moduli spaces
• Mirror symmetry with branes by equivariant Verlinde formulae
• Quiver Asymptotics and Amoeba: Instantons on Toric Divisors of Calabi-Yau Threefolds
• Generating series for the $E$-polynomials of $GL(n,\mathbb{C})$-character varieties