What question did this study set out to answer?

The primary aim is to classify coregularity zero semi log canonical quartic surfaces containing algebraic tori.

January 27, 2026Journal of the London Mathematical Society0 citationsOpen Access

Algebraic tori in the complement of quartic surfaces

ESEduardo Alves da SilvaUniversity of Basel FFFernando FigueroaNorthwestern University JMJoaquin MoragaUniversity of California, Los Angeles

Key Points

The primary aim is to classify coregularity zero semi log canonical quartic surfaces containing algebraic tori.
Initiation of classification process for specific quartic surfaces.
Analysis of algebraic tori embedded in quartic surfaces.
Development of criteria for log Calabi–Yau pairs in toric varieties.
Identification of coregularity zero quartic surfaces that support algebraic tori.
Establishment of equivalencies between algebraic tori and cluster type pairs.
Presentation of criteria to assess cluster type pairs over toric varieties.

Abstract

Abstract 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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