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

Laurent Ducrohet (1)

1 IMJ - Institut de Mathématiques de Jussieu

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.

Mots clés: Frobenius; vector bundles

Domaines: Géométrie algébrique [math.AG]

Laurent Ducrohet. The action of the Frobenius map on rank 2 vector bundles over a supersingular genus 2 curve in characteristic 2.. 2005. ⟨hal-00004795v1⟩