Betti numbers of Brill-Noether varieties on a general curve

Camilla Felisetti; Claudio Fontanari

paper

Betti numbers of Brill-Noether varieties on a general curve

arXiv:2107.11109

Abstract

We compute the rational cohomology groups of the smooth Brill-Noether varieties $G_{d}^{r} (C)$ , 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 $W_{d}^{r} (C)$ , parametrizing complete linear series on $C$ of degree $d$ and dimension at least $r$ .

Final version, to appear in "Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl."