On the p-rank of curves

2020/01/07 by Sadık Terzi, Terzi, Sadık
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2001.03310

openalex publication_date 2020/01/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 \mbPⁿ for~n≥ 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.

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