Hostname: page-component-586b7cd67f-2plfb Total loading time: 0 Render date: 2024-11-24T09:47:48.003Z Has data issue: false hasContentIssue false
  • English
  • Français

Moduli of Vector Bundles on Curves in Positive Characteristics

Published online by Cambridge University Press:  04 December 2007

Kirti Joshi  and
Eugene Z. Xia
Kirti Joshi
Affiliation:
Department of Mathematics, University of Arizona, Tucson, AZ 85721, U.S.A. E-mail: [email protected]
Eugene Z. Xia
Affiliation:
Department of Mathematics, University of Arizona, Tucson, AZ 85721, U.S.A. E-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let X be a projective curve of genus 2 over an algebraically closed field of characteristic 2. The Frobenius map on X induces a rational map on the moduli scheme of rank-2 bundles. We show that up to isomorphism, there is only one (up to tensoring by an order two line bundle) semi-stable vector bundle of rank 2 (with determinant equal to a theta characteristic) whose Frobenius pull-back is not semi-stable. The indeterminacy of the Frobenius map at this point can be resolved by introducing Higgs bundles.

Keywords

algebraic curvesFrobenius morphismmoduli schemesvector bundles
Type
Research Article
Information
Compositio Mathematica , Volume 122 , Issue 3 , July 2000 , pp. 315 - 321
Copyright
© 2000 Kluwer Academic Publishers