Moduli of Vector Bundles on Curves in Positive Characteristics

Details Moduli of Vector Bundles on Curves in Positive Characteristics Moduli of Vector Bundles on Curves in Positive Characteristics

1999-10-04

arxiv.org/abs/math/9910014v1

Mathematics

Algebraic Geometry

Scientific paper

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.

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