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Semipositive bundles and Brill-Noether theory

Vicente Munoz·Francisco Presas
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Abstract

We prove a Lefschetz hyperplane theorem for the determinantal loci of a morphism between two holomorphic vector bundles $E$ and $F$ over a complex manifold under the condition that $E^*\ox F$ is Griffiths $k$-positive. We apply this result to find some homotopy groups of the Brill-Noether loci for a generic curve.

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Vicente Munoz, Francisco Presas. 2001-10-09. Semipositive bundles and Brill-Noether theory. https://arxiv.org/abs/math/0107226

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