The Frobenius map, rank 2 vector bundles and Kummer's quartic surface in characteristic 2 and 3 |
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Authors: | Yves Laszlo |
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Affiliation: | a Université Pierre et Marie Curie, Case 82, Analyse Algébrique, UMR 7586, 4, place Jussieu, 75252 Paris Cedex 05, France b Laboratoire J.-A. Dieudonné, Université de Nice Sophia Antipolis, Parc Valrose, 06108 Nice Cedex 02, France |
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Abstract: | Let X be a smooth projective curve of genus g?2 defined over an algebraically closed field k of characteristic p>0. Let MX(r) be the moduli space of semi-stable vector bundles with fixed trivial determinant. The relative Frobenius map induces by pull-back a rational map . We determine the equations of V in the following two cases (1) (g,r,p)=(2,2,2) and X nonordinary with Hasse-Witt invariant equal to 1 (see math.AG/0005044 for the case X ordinary), and (2) (g,r,p)=(2,2,3). We also show the existence of base points of V, i.e., semi-stable bundles E such that F∗E is not semi-stable, for any triple (g,r,p). |
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Keywords: | Primary 14H60 14D20 Secondary 14H40 |
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