{"paper":{"title":"Algebraic tori in the complement of quartic surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Eduardo Alves da Silva, Fernando Figueroa, Joaqu\\'in Moraga","submitted_at":"2024-11-05T20:46:10Z","abstract_excerpt":"Let $B\\subset \\mathbb{P}^3$ be an slc quartic surface. The existence of an embedding $\\mathbb{G}_m^3\\hookrightarrow \\mathbb{P}^3\\setminus B$ implies that $B$ has coregularity zero. In this article, we initiate the classification of coregularity zero slc quartic surfaces $B\\subset \\mathbb{P}^3$ for which $\\mathbb{P}^3\\setminus B$ contains an algebraic torus $\\mathbb{G}_m^3$. Equivalently, the classification of cluster type pairs $(\\mathbb{P}^3,B)$. Along the way, we give criteria for a log Calabi--Yau pair $(X,B)$ over a toric variety $T$ to be of cluster type."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.03506","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2411.03506/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}