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摘要翻译：
设X是定义在特征为P的代数闭域上的属2（也是属3）的一般真光滑曲线。当3leqpleq7时，Frobenius对具有平凡行列式的秩2半稳定向量丛的作用完全由它对在X上某些2阶线丛作用下不变的30条线（又称126个Kummer曲面）的限制决定。这些线（又称Kummer曲面）与椭圆曲线（又称维数为2的abelian型）密切相关，而椭圆曲线是与X的双重覆盖相关的Prym型）。因此，我们可以在这些情况下计算这种作用的显式方程。我们执行其中一些计算并得出一些结果。
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英文标题：
《The Frobenius action on rank 2 vector bundles over curves in small genus
and small characteristic》
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作者：
Laurent Ducrohet
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最新提交年份：
2008
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分类信息：
一级分类：Mathematics 数学
二级分类：Algebraic Geometry 代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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英文摘要：
Let X be a general proper and smooth curve of genus 2 (resp. of genus 3) defined over an algebraically closed field of characteristic p. When 3\leq p \leq 7, the action of Frobenius on rank 2 semi-stable vector bundles with trivial determinant is completely determined by its restrictions to the 30 lines (resp. the 126 Kummer surfaces) that are invariant under the action of some order 2 line bundle over X. Those lines (resp. those Kummer surfaces) are closely related to the elliptic curves (resp. the abelian varieties of dimension 2) that appear as the Prym varieties associated to double \'etale coverings of X. We are therefore able to compute explicit equations of this action in these cases. We perform some of these computations and draw some consequences.
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PDF链接：
https://arxiv.org/pdf/0803.1380
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