Compactifications of the affine plane over non-closed fields

Published 19 Jul 2021 in math.AG | (2107.08730v4)

Abstract: In this article, 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 non-closed 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.}