Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 21 (2025), 042, 16 pages      arXiv:2405.04862      https://doi.org/10.3842/SIGMA.2025.042

On Degenerations of the Projective Plane

Jürgen Hausen ^a, Katharina Király ^a and Milena Wrobel ^b
a) Mathematisches Institut, Universität Tübingen, Auf der Morgenstelle 10, 72076 Tübingen, Germany
^b) Institut für Mathematik, Universität Oldenburg, 26111 Oldenburg, Germany

Received December 17, 2024, in final form June 07, 2025; Published online June 12, 2025

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.

Key words: degenerations of the plane; Markov numbers; del Pezzo surfaces; torus action.

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