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SEMIPOSITIVE BUNDLES AND BRILL–NOETHER THEORY

Published online by Cambridge University Press:  20 March 2003

VICENTE MUÑOZ  and
FRANCISCO PRESAS
VICENTE MUÑOZ
Affiliation:
Departamento de Matemáticas, Facultad de Ciencias, Universidad Autónoma de Madrid, 28049 Madrid, Spainvicente.munoz@uam.es
FRANCISCO PRESAS
Affiliation:
Mathematics Department. Bldg. 380, Stanford University, Stanford, CA 90304, USAfpresas@math.stanford.edu Departamento de Álgebra, Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid, 28040 Madrid, Spainfpm@eucmos.sim.ucm.es
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Abstract

A Lefschetz hyperplane theorem for the determinantal loci of a morphism between two holomorphic vector bundles $E$ and $F$ over a complex manifold is proved, under the condition that $E^* \otimes F$ is Griffiths $k$-positive. This result is applied to find some homotopy groups of the Brill–Noether loci for a generic curve.

Keywords

32Q5514M1214H51
Type
NOTES AND PAPERS
Information
Bulletin of the London Mathematical Society , Volume 35 , Issue 2 , March 2003 , pp. 179 - 190
Copyright
© The London Mathematical Society 2003

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Footnotes

Partially supported by The European Contract Human Potential Programme, Research Training Network HPRN-CT-2000-00101.