ON THE p-RANK OF CURVES

TERZİ S.

Proceedings of the American Mathematical Society, vol.152, no.10, pp.4155-4169, 2024 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 152 Issue: 10
  • Publication Date: 2024
  • Doi Number: 10.1090/proc/16841
  • Journal Name: Proceedings of the American Mathematical Society
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH, DIALNET
  • Page Numbers: pp.4155-4169
  • Keywords: complete intersections, Hirzebruch surfaces, p-Rank
  • Middle East Technical University Affiliated: Yes

Abstract

In this paper, we are concerned with the computations of the prank of curves in two different setups. We first work with complete intersection varieties in Pn 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 pg(S) = 0 = q(S) such as Hirzebruch surfaces and determine p-rank of curves on Hirzebruch surfaces.