Betti numbers of Brill-Noether varieties on a general curve
Abstract
We compute the rational cohomology groups of the smooth Brill-Noether varieties Grd(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 Wrd(C), parametrizing complete linear series on C of degree d and dimension at least r.
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