Moduli of Vector Bundles on Curves in Positive Characteristics

Kirti Joshi, Eugene Z. Xia

Research output: Contribution to journalArticlepeer-review

12 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)315-321
Number of pages7
JournalCompositio Mathematica
Volume122
Issue number3
DOIs
StatePublished - 2000

Keywords

  • Algebraic curves
  • Frobenius morphism
  • Moduli schemes
  • Vector bundles

ASJC Scopus subject areas

  • Algebra and Number Theory

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