Moduli of Vector Bundles on Curves in Positive Characteristics

1999/10/04 by Kirti Joshi, Joshi, Kirti, Eugene Z. Xia +1 · 1 citation
Engineering · Mathematics · #14D20 #14H60 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Differential Equations and Numerical Methods #FOS: Mathematics #Material Science and Thermodynamics #math.AG #msc:14D20 #msc:14H60

paper · pdf · doi:10.48550/arxiv.math/9910014

arxiv created 1999/10/04 · openalex publication_date 1999/10/04 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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• Explicit computation of the generic degree of the generalized Verschiebung in rank two

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