Tropical methods for stable Horikawa surfaces

Evans, Jonny and Simonetti, Angelica and Urzua, Giancarlo (2024) Tropical methods for stable Horikawa surfaces. arXiv.

Abstract

There are many strata in the KSBA boundary of the moduli space of octic double planes (K2=2, pg=3). We use methods from tropical and toric geometry to show that only three of these correspond to surfaces with at worst quotient singularities.