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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
90/2019

Towards classifying toric degenerations of cubic surfaces

Maria Donten-Bury, Paul Görlach and Milena Wrobel

Abstract

We investigate degenerations of cubic surfaces which are obtained from degenerating their Cox rings to toric algebras. We work in the spirit of Sturmfels and Xu who use the theory of Khovanskii bases to determine toric degenerations of Del Pezzo surfaces of degree 4 and leave the question of classifying these degenerations in the degree 3 case as an open problem. We describe an approach for the classification which is closely related to tropical geometry and present partial results in this direction.

Received:
26.09.19
Published:
27.09.19
Keywords:
cubic surface, del Pezzo surface, Cox ring, Toric degeneration, tropicalization

Related publications

inJournal
2020 Journal Open Access
Maria Donten-Bury, Paul Görlach and Milena Wrobel

Towards classifying toric degenerations of cubic surfaces

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