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arXiv · 2107.11109

Betti numbers of Brill-Noether varieties on a general curve

Camilla Felisetti·Claudio Fontanari
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Abstract

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 $r$.

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Camilla Felisetti, Claudio Fontanari. 2021-09-23. Betti numbers of Brill-Noether varieties on a general curve. https://arxiv.org/abs/2107.11109

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