Betti numbers of Brill-Noether varieties on a general curve

2021/07/23 by Camilla Felisetti, Felisetti, Camilla, Claudio Fontanari +1
Mathematics · #Advanced Combinatorial Mathematics #Commutative Algebra and Its Applications #Algebraic Geometry and Number Theory

paper · pdf · doi:10.48550/arxiv.2107.11109

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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