Jürgen Hausen, Katharina Király, Milena Wrobel, “On Degenerations of the Projective Plane”, SIGMA, 2025, Volume 21,042, 16 pp.

On Degenerations of the Projective Plane

Jürgen Hausen^a, Katharina Király^a, Milena Wrobel^b

^a Mathematisches Institut, Universität Tübingen, Auf der Morgenstelle 10, 72076 Tübingen, Germany
^b Institut für Mathematik, Universität Oldenburg, 26111 Oldenburg, Germany

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.

Keywords: degenerations of the plane, Markov numbers, del Pezzo surfaces, torus action.

MSC: 14L30, 14J26, 14J10, 14D06

Received: December 17, 2024; in final form June 7, 2025; Published online June 12, 2025

Language: English

DOI: 10.3842/SIGMA.2025.042