The Hodge--Poincaré polynomial of the moduli spaces of stable vector bundles over an algebraic curve

Abstract

Let X be a nonsingular complex projective variety that is acted on by a reductive group $G$ and such that $X^{ss}\ne X_{(0)}^s\ne \varnothing$. We give formulae for the Hodge--Poincaré series of the quotient $X_{(0)}^s/G$. We use these computations to obtain the corresponding formulae for the Hodge--Poincaré polynomial of the moduli space of properly stable vector bundles when the rank and the degree are not coprime. We compute explicitly the case in which the rank equals 2 and the degree is even.

Final published version. arXiv admin note: text overlap with arXiv:math/0305346, arXiv:math/0305347 by other authors

References in corpus (1)

• Moduli spaces of bundles over Riemann surfaces and the Yang-Mills stratification revisited

Cited by in corpus (2)

• Pseudo-quotients of algebraic actions and their application to character varieties
• Hodge polynomials of some moduli spaces of Coherent Systems