Algebraic tori in the complement of quartic surfaces
| Autor: | da Silva, Eduardo Alves, Figueroa, Fernando, Moraga, Joaquín |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 24 pages |
| Databáze: | arXiv |
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