Betti numbers of Brill-Noether varieties on a general curve

Camilla Felisetti; Claudio Fontanari

Betti numbers of Brill-Noether varieties on a general curve

Algebraic Geometry 2021-09-24 v2

Authors: Camilla Felisetti , Claudio Fontanari

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 $r$ .

Keywords

Brill-Noether varieties Betti numbers rational cohomology general curve intersection cohomology linear series

Cite

@article{arxiv.2107.11109,
  title  = {Betti numbers of Brill-Noether varieties on a general curve},
  author = {Camilla Felisetti and Claudio Fontanari},
  journal= {arXiv preprint arXiv:2107.11109},
  year   = {2021}
}

Comments

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

Betti numbers of Brill-Noether varieties on a general curve

Abstract

Keywords

Cite

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