Quartic surfaces up to volume preserving equivalence

TL;DR

This paper classifies log Calabi--Yau pairs with quartic surfaces in projective 3-space up to volume preserving equivalence, revealing that maximal pairs admit toric models, advancing understanding of their geometric structure.

Contribution

It provides a classification of quartic log Calabi--Yau pairs with low coregularity and demonstrates the existence of toric models for maximal pairs.

Findings

Classification of pairs with coregularity ≤ 1

Maximal pairs have toric models

Complete description of volume preserving equivalence classes

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.