Semipositive bundles and Brill-Noether theory
arXiv:math/0107226
Abstract
We prove a Lefschetz hyperplane theorem for the determinantal loci of a morphism between two holomorphic vector bundles and over a complex manifold under the condition that $E^*\ox F$ is Griffiths -positive. We apply this result to find some homotopy groups of the Brill-Noether loci for a generic curve.
(one small mistake corrected)