On the cohomology of Brill-Noether loci over Quot schemes
Algebraic Geometry
2008-04-07 v4
Abstract
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.
Keywords
Cite
@article{arxiv.math/0602491,
title = {On the cohomology of Brill-Noether loci over Quot schemes},
author = {Cristina Martinez Ramirez},
journal= {arXiv preprint arXiv:math/0602491},
year = {2008}
}