论文标题
在曲线的P级
On the p-rank of curves
论文作者
论文摘要
在本文中，我们关注的是两个不同设置的曲线的计算。我们首先在$ \ mb {p}^n \ text {for} 〜n \ ge 2 $中使用完整的交点品种，并明确计算Frobenius对顶级同胞组的作用。在曲线和表面的情况下，此信息足以确定该品种是否普通。接下来，我们考虑使用$ p_g（s）= 0 = q（s）$（例如Hirzebruch表面）上的曲线，并确定Hirzebruch表面上曲线的$ p $ lank。
In this paper, we are concerned with the computations of the $p$-rank of curves in two different setups. We first work with complete intersection varieties in $\mb{P}^n \text{ for}~n\ge 2$ and compute explicitly the action of Frobenius on the top cohomology group. In case of curves and surfaces, this information suffices to determine if the variety is ordinary. Next, we consider curves on more general surfaces with $p_g(S) = 0 = q(S)$ such as Hirzebruch surfaces and determine $p$-rank of curves on Hirzebruch surfaces.
