The action of the Frobenius map on rank 2 vector bundles in characteristic 2

Details The action of the Frobenius map on rank 2 vector bundles in characteristic 2 The action of the Frobenius map on rank 2 vector bundles in characteristic 2

2000-05-04

arxiv.org/abs/math/0005044v1

Mathematics

Algebraic Geometry

19 pages

Scientific paper

Let $X$ be an ordinary smooth curve defined over an algebraically closed field of characteristic 2. The absolute Frobenius induces a rational map $F$ on the moduli space $M_X$ of rank 2 vector bundles with fixed trivial determinant. If the genus of $X$ is 2, the moduli space $M_X$ is isomorphic to projective space of dimension 3 (as over the complex numbers). In this case we explicitly give the equations of $F$, which enables us to determine, for example, its base locus (one point) and its image (different from $M_X$).

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