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Wallcrossing and Cohomology of The Moduli Space of Hitchin Pairs

Wu-yen Chuang, Duiliu-Emanuel Diaconescu, Guang Pan

Abstract

A conjectural recursive relation for the Poincaré polynomial of the Hitchin moduli space is derived from wallcrossing in the refined local Donaldson-Thomas theory of a curve. A doubly refined generalization of this theory is also conjectured and shown to similarly determine the Hodge polynomial of the same moduli space.

Wallcrossing and Cohomology of The Moduli Space of Hitchin Pairs

Abstract

A conjectural recursive relation for the Poincaré polynomial of the Hitchin moduli space is derived from wallcrossing in the refined local Donaldson-Thomas theory of a curve. A doubly refined generalization of this theory is also conjectured and shown to similarly determine the Hodge polynomial of the same moduli space.