JournalsrlmVol. 33, No. 1pp. 65–72

Betti numbers of Brill–Noether varieties on a general curve

  • Camilla Felisetti

    Università di Trento, Italy
  • Claudio Fontanari

    Università di Trento, Italy
Betti numbers of Brill–Noether varieties on a general curve cover
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Abstract

We compute the rational cohomology groups of the smooth Brill–Noether varieties Gdr(C)G^r_d(C), parametrizing linear series of degree dd and dimension exactly rr on a general curve CC. As an application, we determine the whole intersection cohomology of the singular Brill–Noether loci Wdr(C)W^r_d(C), parametrizing complete linear series on CC of degree dd and dimension at least rr.

Cite this article

Camilla Felisetti, Claudio Fontanari, Betti numbers of Brill–Noether varieties on a general curve. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 33 (2022), no. 1, pp. 65–72

DOI 10.4171/RLM/964