On vector bundles destabilized by Frobenius pull-back

Kirti Joshi, S. Ramanan, Eugene Z. Xia, Jiu Kang Yu

Research output: Contribution to journalArticlepeer-review

31 Scopus citations

Abstract

Let X be a smooth projective curve of genus g > 1 over an algebraically closed field of positive characteristic. This paper is a study of a natural stratification, defined by the absolute Frobenius morphism of X, on the moduli space of vector bundles. In characteristic two, there is a complete classification of semi-stable bundles of rank 2 which are destabilized by Frobenius pull-back. We also show that these strata are irreducible and obtain their respective dimensions. In particular, the dimension of the locus of bundles of rank two which are destabilized by Frobenius is 3g-4. These Frobenius destabilized bundles also exist in characteristics two, three and five with ranks 4, 3 and 5, respectively. Finally, there is a connection between (pre)-opers and Frobenius destabilized bundles. This allows an interpretation of some of the above results in terms of pre-opers and provides a mechanism for constructing Frobenius destabilized bundles in large characteristics.

Original languageEnglish (US)
Pages (from-to)616-630
Number of pages15
JournalCompositio Mathematica
Volume142
Issue number3
DOIs
StatePublished - 2006

Keywords

  • Characteristic p
  • Frobenius morphism
  • Protective curves

ASJC Scopus subject areas

  • Algebra and Number Theory

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