Quartic surfaces up to volume preserving equivalence

Abstract

We study log Calabi--Yau pairs of the form $({\mathbb{P}}^3,\Delta )$, where $\Delta$ is a quartic surface, and classify all such pairs of coregularity less than or equal to one, up to volume preserving equivalence. In particular, if $({\mathbb{P}}^3,\Delta )$ is a maximal log Calabi--Yau pair then we show that it has a toric model.

arXiv comment21 pages