Work

Non-log Liftable Log Del Pezzo Surfaces of Rank One in Characteristic Five

Year: 2025

Type: article

Abstract: Building upon the classification by Lacini, we determine the isomorphism classes of log del Pezzo surfaces of rank one over an algebraically closed field of characteristic five either which are not log liftable over the ring of Witt vectors or whose singularities are not feasible in characteristic zero. We also show that such a surface is always constructed from the Du Val del Pezzo surface of Dynkin type $2[2^4]$ . Furthermore, We show that the Kawamata–Viehweg vanishing theorem for ample $\mathbb {Z}$ -Weil divisors holds for log del Pezzo surfaces of rank one in characteristic five if those singularities are feasible in characteristic zero.

Source: Nagoya Mathematical Journal

DOI: 10.1017/nmj.2024.37

Author: MASARU NAGAOKA

Institution: Gakushuin University

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Japan Society for the Promotion of Science

Award: アフィンホモロジー胞体とそのコンパクト化の研究