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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
Authors
Makoto Enokizono
Department of Mathematics
College of Science
Rikkyo University
Tokyo
Japan

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