Vanishing theorems and adjoint linear systems on normal surfaces in positive characteristic

Makoto Enokizono

Vol. 324 (2023), No. 1, 71–110

DOI: 10.2140/pjm.2023.324.71

Abstract

We prove the Kawamata–Viehweg vanishing theorem for a large class of divisors on surfaces in positive characteristic. By using this vanishing theorem, Reider-type theorems and extension theorems of morphisms for normal surfaces are established. As an application of the extension theorems, we characterize nonsingular rational points on any plane curve over an arbitrary base field in terms of rational functions on the curve.

Keywords

vanishing theorem, adjoint linear system, extension theorem, plane curve

Mathematical Subject Classification

Primary: 14C20, 14F17, 14G05

Milestones

Received: 21 August 2022

Revised: 26 March 2023

Accepted: 1 May 2023

Published: 22 June 2023