Betti numbers of Brill-Noether varieties on a general curve (Q2154795)

Summary: We compute the rational cohomology groups of the smooth Brill-Noether varieties \(G^r_d(C)\), 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 \(r\).