Let X be a nonsingular complex projective variety that is acted on by a reductive group $G$ and such that $X^{ ss} \neq X_{ (0)}^{ s}\neq \emptyset$. We give formulae for the Hodge--Poincar\'e series of the quotient $X_{ (0)}^s/G$. We use these computations to obtain the corresponding formulae for the Hodge--Poincar\'e 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.
Categories: math.AG