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 language | English (US) |
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Pages (from-to) | 315-321 |
Number of pages | 7 |
Journal | Compositio Mathematica |
Volume | 122 |
Issue number | 3 |
DOIs | |
State | Published - 2000 |
Keywords
- Algebraic curves
- Frobenius morphism
- Moduli schemes
- Vector bundles
ASJC Scopus subject areas
- Algebra and Number Theory