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Frobenius pull-back and stability of vector bundles in characteristic 2

Jiu-Kang Yu·Eugene Z. Xia
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Abstract

Let X be a smooth projective curve of genus g>1 over an algebraically closed field of characteristic 2. Pull-back by the (absolute) Frobenius on X only defines a rational morphism on the moduli scheme of rank-2 vector bundles on X, because the Frobenius pull-back may destory stability of a vector bundle. This paper introduces and studies a Harder-Narasimhan type stratification on the moduli scheme and proves that the family of semi-stable rank-2 vector bundles (with a fixed degree) whose Frobenius pull-back are not semi-stable is parameterized by an irreducible subscheme of dimension 3g-4.

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Jiu-Kang Yu, Eugene Z. Xia. 2001-11-07. Frobenius pull-back and stability of vector bundles in characteristic 2. https://arxiv.org/abs/math/0111068

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