On the 𝑝-rank of curves

Pub Date : 2024-03-29 DOI:10.1090/proc/16841

Sadik Terzİ

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引用次数: 0

Abstract

In this paper, we are concerned with the computations of the p p -rank of curves in two different setups. We first work with complete intersection varieties in P n for n ≥ 2 \mathbf {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 ) p_g(S) = 0 = q(S) such as Hirzebruch surfaces and determine p p -rank of curves on Hirzebruch surfaces.

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论曲线的𝑝-rank

在本文中，我们关注两种不同情况下曲线 p p -rank 的计算。我们首先处理 n ≥ 2 \mathbf {P}^n \text { for } n\ge 2 的 P n 中的完全交集品种，并明确计算 Frobenius 对顶同调群的作用。在曲线和曲面的情况下，这些信息足以确定该变化是否普通。接下来，我们考虑更一般的曲面上的曲线，即 p g ( S ) = 0 = q ( S ) p_g(S) = 0 = q(S)，如希尔泽布鲁赫曲面，并确定希尔泽布鲁赫曲面上曲线的 p p -rank。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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