We compute the rational cohomology groups of the smooth Brill–Noether varieties Gr 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.
Betti numbers of Brill–Noether varieties on a general curve / Felisetti, Camilla; Fontanari, Claudio. - In: ATTI DELLA ACCADEMIA NAZIONALE DEI LINCEI. RENDICONTI LINCEI. MATEMATICA E APPLICAZIONI. - ISSN 1120-6330. - 2022/33:1(2022), pp. 65-72. [10.4171/RLM/964]
Betti numbers of Brill–Noether varieties on a general curve
Felisetti, Camilla;Fontanari, Claudio
2022-01-01
Abstract
We compute the rational cohomology groups of the smooth Brill–Noether varieties Gr 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.| File | Dimensione | Formato | |
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