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Moduli of vector bundles on curves in positive characteristic

Kirti Joshi·Eugene Z. Xia
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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 space 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 stable. The indeterminacy of the Frobenius map at this point can be resolved by introducing Higgs bundles.

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Kirti Joshi, Eugene Z. Xia. 1998-09-18. Moduli of vector bundles on curves in positive characteristic. https://arxiv.org/abs/math/9809106

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