The Frobenius map, rank 2 vector bundles and Kummer's quartic surface in characteristic 2 and 3

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• 作者：Laszlo ; Yves ; Pauly ; Christian
• 关键词：Primary 14H60 ; 14D20 ; Secondary 14H40
• 刊名：Advances in Mathematics
• 出版年：2004
• 期刊代码：62_00018708
• 类别：mt
• 出版时间：July 10, 2004
• 卷：185
• 期：2
• 页码：246-269
• 文件大小：275 K

摘要

Let X be a smooth projective curve of genus g≥2 defined over an algebraically closed field k of characteristic p>0. Let M_X(r) be the moduli space of semi-stable rankr vector bundles with fixed trivial determinant. The relative Frobenius map F:X→X₁ induces by pull-back a rational map V:M_X1(r)→M_X(r). 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).