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This article classifies coregularity zero quartic surfaces with algebraic tori, indicating potential for deeper understanding of their geometric properties.
Let be an slc quartic surface. The existence of an embedding implies that has coregularity zero. In this article, we initiate the classification of coregularity zero semi log canonical (slc) quartic surfaces for which contains an algebraic torus , and equivalently, the classification of cluster type pairs . Along the way, we give criteria for a log Calabi–Yau pair over a toric variety to be of cluster type.
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Silva et al. (2026) studied this question.
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