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Moduli of Vector Bundles on Curves in Positive Characteristics

Published online by Cambridge University Press:  04 December 2007

Kirti Joshi  and
Eugene Z. Xia
Kirti Joshi
Affiliation:
Department of Mathematics, University of Arizona, Tucson, AZ 85721, U.S.A. E-mail: kirti@math.Arizona.edu
Eugene Z. Xia
Affiliation:
Department of Mathematics, University of Arizona, Tucson, AZ 85721, U.S.A. E-mail: exia@math.Arizona.edu
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Abstract

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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.

Keywords

algebraic curvesFrobenius morphismmoduli schemesvector bundles
Type
Research Article
Information
Compositio Mathematica , Volume 122 , Issue 3 , July 2000 , pp. 315 - 321
Copyright
© 2000 Kluwer Academic Publishers