Nonemptiness of Brill–Noether loci in M(2,L)-Reference-Cited by-同舟云学术

Nonemptiness of Brill–Noether loci in M(2,L)

Published:2015-12 Issue:13 Volume:26 Page:1550108
ISSN:0129-167X
Container-title:International Journal of Mathematics
language:en
Short-container-title:Int. J. Math.

Author:

Lange H.¹,Newstead P. E.²,Strehl V.³

Affiliation:

1. Department Mathematik, Universität Erlangen-Nürnberg Cauerstrasse 11, D-91058 Erlangen, Germany

2. Department of Mathematical Sciences, University of Liverpool, Peach Street, Liverpool L69 7ZL, UK

3. Department Informatik, Universität Erlangen-Nürnberg Martensstrasse 3, D-91058 Erlangen, Germany

Abstract

Let [Formula: see text] be a smooth projective complex curve of genus [Formula: see text]. We investigate the Brill–Noether locus consisting of stable bundles of rank 2 and determinant [Formula: see text] of odd degree [Formula: see text] having at least [Formula: see text] independent sections. This locus possesses a virtual fundamental class. We show that in many cases this class is nonzero, which implies that the Brill–Noether locus is nonempty. For many values of [Formula: see text] and [Formula: see text] the result is best possible. We obtain more precise results for [Formula: see text]. Appendix A contains the proof of a combinatorial lemma which we need.

Publisher

World Scientific Pub Co Pte Lt

Subject

General Mathematics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0129167X15501086

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