On Degenerations of the Projective Plane

TL;DR

This paper explicitly classifies all log terminal, rational degenerations of the projective plane that admit a non-trivial torus action, extending previous results in the field.

Contribution

It provides an explicit classification of certain degenerations of the projective plane, complementing and extending prior work by Hacking and Prokhorov.

Findings

Complete list of degenerations with torus action

Explicit descriptions of each degeneration

Extension of previous classification results

Abstract

Complementing results of Hacking and Prokhorov, we determine in an explicit manner all log terminal, rational, degenerations of the projective plane that allow a non-trivial torus action.