Compactifications of the affine plane over nonclosed fields

Masatomo Sawahara

Vol. 321 (2022), No. 2, 375–413

DOI: 10.2140/pjm.2022.321.375

Abstract

We give the classification of normal del Pezzo surfaces of rank one with at most log canonical singularities containing the affine plane defined over an algebraically nonclosed field of characteristic zero. As an application, we have a criterion for del Pezzo fibrations with canonical singularities whose generic fibers are not smooth to contain vertical ${\mathbb{𝔸}}^2$-cylinders.

Keywords

normal del Pezzo surface, compactification of the affine plane, algebraically nonclosed field

Mathematical Subject Classification

Primary: 14J26

Secondary: 14J17, 14J45, 14R10

Milestones

Received: 16 May 2022

Revised: 25 October 2022

Accepted: 31 October 2022

Published: 21 March 2023