On the cohomology of Brill-Noether loci over Quot schemes

Details On the cohomology of Brill-Noether loci over Quot schemes On the cohomology of Brill-Noether loci over Quot schemes

2006-02-22

arxiv.org/abs/math/0602491v4

Journal of Algebra, Vol 319/10 (2008), pp 4391-4403

Mathematics

Algebraic Geometry

Scientific paper

Let C be a smooth projective curve over the field of the complex numbers. We consider Brill-Noether loci over the moduli of maps from C to the Grassmannian G(m,n) and the corresponding Quot schemes of quotients of a trivial vector bundle on C compactifying the spaces of morphisms. We study in detail the case in which m=2, n=4. We prove results on the irreducibility and dimension of these Brill-Noether loci and we address explicit formulas for their cohomology classes. We study the existence problem of these spaces which is closely related with the problem of classification of vector bundles over curves.

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