Algebraic tori in the complement of quartic surfaces
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866910686503763968 |
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| author | da Silva, Eduardo Alves Figueroa, Fernando Moraga, Joaquín |
| author_facet | da Silva, Eduardo Alves Figueroa, Fernando Moraga, Joaquín |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_03506 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Algebraic tori in the complement of quartic surfaces da Silva, Eduardo Alves Figueroa, Fernando Moraga, Joaquín Algebraic Geometry 14M25, 14E25 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. |
| title | Algebraic tori in the complement of quartic surfaces |
| topic | Algebraic Geometry 14M25, 14E25 |
| url | https://arxiv.org/abs/2411.03506 |