Frobenius stable pluricanonical systems on threefolds of general type in positive characteristic

Zhang, Lei

doi:10.2140/ant.2022.16.2339

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Frobenius stable pluricanonical systems on threefolds of general type in positive characteristic

Lei Zhang

Vol. 16 (2022), No. 10, 2339–2384

DOI: 10.2140/ant.2022.16.2339

Abstract

This paper investigates effectivity problems of pluricanonical systems on varieties of general type in positive characteristic. In practice, we will consider a sublinear system $| S_{-}^{0} (X, K_{X} + n K_{X}) | \subseteq | H^{0} (X, K_{X} + n K_{X}) |$ generated by certain Frobenius stable sections, and prove that for a minimal terminal threefold $X$ of general type with either $q (X) > 0$ or Gorenstein singularities, if $n \geq 28$ then $| S_{-}^{0} (X, K_{X} + n K_{X}) | \neq \emptyset$ ; and if $n \geq 42$ then the linear system $| S_{-}^{0} (X, K_{X} + n K_{X}) |$ defines a birational map.

Keywords

effectivity problems, pluricanonical systems, positive characteristic, Frobenius stable sections

Mathematical Subject Classification

Primary: 14E05, 14E30

Milestones

Received: 27 February 2021

Revised: 5 January 2022

Accepted: 18 February 2022

Published: 28 January 2023

Authors

Lei Zhang
School of Mathematical Science University of Science and Technology of China Hefei China

Vol. 16, No. 10, 2022