# Toric Degenerations of Cubic Surfaces¶

This website contains auxiliary material to the article:

Maria Donten-Bury, Paul Görlach, and Milena Wrobel: Towards classifying toric degenerations of cubic surfaces

In: Le Matematiche, 75 (2020) 2, p. 537-557

MIS-Preprint: 90/2019 DOI: 10.4418/2020.75.2.9 ARXIV: https://arxiv.org/abs/1909.06690 CODE: https://mathrepo.mis.mpg.de/ToricDegenerationsCubics

Theorem 4.1 of this article describes a fan structure on the tropical variety TGr(3,6) adapted to the classification of Khovanskii bases. The following Singular code generates this fan structure and extracts information about moneric classes. The main results of the computation are stated in Section 4 of the above article. Exhaustive output is provided below.

Output:

38 of these combinatorial types lead to toric degenerations. The following Macaulay2 code computes them by filtering out which moneric classes from the above output form a Khovanskii basis. We output the choices of initial monomials and the corresponding toric ideals.

Output:

Last update: December 9, 2019