The action of the Frobenius map on rank 2 vector bundles over a supersingular genus 2 curve in characteristic 2

Details The action of the Frobenius map on rank 2 vector bundles over a supersingular genus 2 curve in characteristic 2 The action of the Frobenius map on rank 2 vector bundles over a supersingular genus 2 curve in characteristic 2

2005-04-25

arxiv.org/abs/math/0504500v2

Mathematics

Algebraic Geometry

15 pages, submitted in april 2005

Scientific paper

Let $X$ be a smooth proper genus 2 curve over an algebraically closed field of characteristic 2. The absolute Frobenius induces a rational map $F$ on the the moduli space $M\_X$ of semi-stable rank 2 vector bundles over $X$, which is isomorphic to a 3-dimensional projective space. Y. Laszlo and C. Pauly recently gave the equations of $F$ for an ordinary $X$. Using deformation, we give these equations for a supersingular $X$ and draw some consequences such as the base locus of $F$ (one point), or the stability of the complementary Zariski open set.

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