Betti numbers of Brill–Noether varieties on a general curve

Abstract

We compute the integral cohomology groups of the smooth Brill-Noether varieties G d (C), parametrizing linear series of degree d and dimension exactly r on a general curve C. As an application, we determine the whole intersection cohomology of the singular Brill-Noether loci W r d (C), parametrizing complete linear series on C of degree d and dimension at least r.