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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 lessthan 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 ithas a toric model.

Quartic surfaces up to volume preserving equivalence