Semipositive bundles and Brill-Noether theory

Mathematics – Differential Geometry

Scientific paper

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(one small mistake corrected)

Scientific paper

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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