A review of Lacini's classification of rank one log del Pezzo surfaces in characteristic different from two and three

Masaru Nagaoka

Paper

A review of Lacini's classification of rank one log del Pezzo surfaces in characteristic different from two and three

Abstract

This paper reviews Lacini's classification [Lac24] of log del Pezzo surfaces of rank one in characteristics different from two and three, with a focus on where and how Lacini enhanced the techniques of Keel and McKernan [KM99]. We point out that there is at most one log del Pezzo surface that may have been erroneously omitted from the list in [Lac24, §6.1], namely the surface in Example 3.13. We also extend the results of [Lac24 §4.2] to arbitrary characteristic.