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Semipositive bundles and Brill-Noether theory

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dc.contributor.authorMuñoz, Vicente
dc.contributor.authorPresas , Francisco
dc.date.accessioned2023-06-20T17:04:04Z
dc.date.available2023-06-20T17:04:04Z
dc.date.issued2003
dc.description.abstractA 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* x F is Griffiths k-positive. This result is applied to find some homotopy groups of the Brill-Noether loci for a generic curve.
dc.description.departmentDepto. de Álgebra, Geometría y Topología
dc.description.facultyFac. de Ciencias Matemáticas
dc.description.refereedTRUE
dc.description.statuspub
dc.eprint.idhttps://eprints.ucm.es/id/eprint/17152
dc.identifier.doi10.1112/S0024609302001741
dc.identifier.issn0024-6093
dc.identifier.officialurlhttp://journals.cambridge.org/abstract_S0024609302001741
dc.identifier.relatedurlhttp:www.cambridge.org
dc.identifier.urihttps://hdl.handle.net/20.500.14352/57717
dc.issue.number2
dc.journal.titleBulletin of the London Mathematical Society
dc.language.isoeng
dc.page.final190
dc.page.initial179
dc.publisherLondon Mathematical society
dc.rights.accessRightsopen access
dc.subject.cdu512.7
dc.subject.cdu5151.1
dc.subject.keywordAmple bundle
dc.subject.keywordLefschetz hyperplane theorem
dc.subject.keywordDeterminantal locus
dc.subject.keywordGriffiths k-positive
dc.subject.keywordBrill-Noether loci
dc.subject.ucmGeometria algebraica
dc.subject.ucmTopología
dc.subject.unesco1201.01 Geometría Algebraica
dc.subject.unesco1210 Topología
dc.titleSemipositive bundles and Brill-Noether theory
dc.typejournal article
dc.volume.number35
dcterms.referencesA. Andreotti and T. Fraenkel, The Lefschetz theorem on hyperplane sections, Annals Math. (2)69 (1959) 713–717. E. Arbarello, M. Cornalba, P. A. Griffiths and J. Harris, Geometry of algebraic curves, Springer-Verlag, New York (1985). R. Bott, On a theorem of Lefschetz, Michigan Math. J. 6 (1959) 211–216. O. Debarre, Lefschetz theorems for degeneracy loci, Bull. Soc. Math. France 128 (2000) 283–308. W. Fulton and R. Lazarsfeld, On the connectedness of degeneracy loci and special divisors, Acta Math. 146 (1981) 271–283. P. A. Griffiths, Hermitian differential geometry, Chern classes and positive vector bundles in Global Analysis,Princeton University Press, Princeton, N.J. (1969). Y-T. Siu, Complex-analyticity of harmonic maps, vanishing and Lefschetz theorems, J. Diff.Geom. 17 (1982) 55–138. P. Griffiths and J. Harris, Principles of Algebraic Geometry, Wiley-Interscience, New York (1978) W-K. To and L. Weng, Curvature of the L2-metric on the direct image of a family of Hermitian-Einstein vector bundles, Amer. J. Math. 120 (1998) 649–661. R. Wells, Differential Analysis on Complex Manifolds, Prentice-Hall, Englewood Cliffs, N.J.,2nd ed. Springer-Verlag (1973).
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