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In this paper we survey geometric and arithmetic techniques to study the cohomology of semiprojective hyperkahler manifolds including toric hyperkahler varieties, Nakajima quiver varieties and moduli spaces of Higgs bundles on Riemann surfaces. The resulti ...
We give a cohomological interpretation of both the Kac polynomial and the refined Donaldson-Thomas-invariants of quivers. This interpretation yields a proof of a conjecture of Kac from 1982 and gives a new perspective on recent work of Kontsevich Soibelman ...
Given a possibly reducible and non-reduced spectral cover pi: X -> C over a smooth projective complex curve C we determine the group of connected components of the Prym variety Prym(X/C). As an immediate application we show that the finite group of n-torsi ...
In this paper we determine the motivic class---in particular, the weight polynomial and conjecturally the Poincar'e polynomial---of the open de Rham space, defined and studied by Boalch, of certain moduli of irregular meromorphic connections on the trivia ...
We study connections between the topology of generic character varieties of fundamental groups of punctured Riemann surfaces, Macdonald polynomials, quiver representations, Hilbert schemes on C-x x C-x, modular forms and multiplicities in tensor products o ...
In this paper we determine the motivic class---in particular, the weight polynomial and conjecturally the Poincaré polynomial---of the open de Rham space, defined and studied by Boalch, of certain moduli of irregular meromorphic connections on the trivial ...
