Frobenius pull-back and stability of vector bundles in characteristic 2

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

Let X be a smooth projective curve of genus g>1 over an algebraically closed field of characteristic 2. Pull-back by the (absolute) Frobenius on X only defines a rational morphism on the moduli scheme of rank-2 vector bundles on X, because the Frobenius pull-back may destory stability of a vector bundle. This paper introduces and studies a Harder-Narasimhan type stratification on the moduli scheme and proves that the family of semi-stable rank-2 vector bundles (with a fixed degree) whose Frobenius pull-back are not semi-stable is parameterized by an irreducible subscheme of dimension 3g-4.
pdf, 9 pages

Keywords

Algebraic Geometry, 14D20, 14H60

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/62578

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0111068
 http://arxiv.org/abs/math/0111068

Collections

arXiv