Muñoz Velazquez, Vicente and Presas , Francisco (2003) Semipositive bundles and Brill-Noether theory. Bulletin of the London Mathematical Society, 35 (2). pp. 179-190. ISSN 0024-6093
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Official URL: http://journals.cambridge.org/abstract_S0024609302001741
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* x F is Griffiths k-positive. This result is applied to find some homotopy groups of the Brill-Noether loci for a generic curve.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | Ample bundle; Lefschetz hyperplane theorem; Determinantal locus; Griffiths k-positive; Brill-Noether loci |
| Subjects: | Sciences > Mathematics > Algebraic geometry Sciences > Mathematics > Topology |
| ID Code: | 17152 |
| References: | A. 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). |
| Deposited On: | 20 Nov 2012 13:48 |
| Last Modified: | 08 May 2013 13:02 |
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