Birational geometry of Calabi-Yau pairs $(\mathbb{P}^3, D)$ of coregularity 2
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866910339057057792 |
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| author | da Silva, Eduardo Alves |
| author_facet | da Silva, Eduardo Alves |
| contents | This paper aims to study the birational geometry of log Calabi-Yau pairs$(\mathbb{P}^3, D)$ of coregularity 2, where in this case $D$ is an irreducible normal quartic surface with canonical singularities. We completely classify which toric weighted blowups of a point will initiate a volume preserving Sarkisov link starting with this pair. Depending on the type of singularity, our results point out that some of these weights do not work generically for a general member of the corresponding coarse moduli space of quartics. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2402_13970 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Birational geometry of Calabi-Yau pairs $(\mathbb{P}^3, D)$ of coregularity 2 da Silva, Eduardo Alves Algebraic Geometry 14E05, 14E07 (Primary) 14E30, 14J17, 14J30 (Secondary) This paper aims to study the birational geometry of log Calabi-Yau pairs$(\mathbb{P}^3, D)$ of coregularity 2, where in this case $D$ is an irreducible normal quartic surface with canonical singularities. We completely classify which toric weighted blowups of a point will initiate a volume preserving Sarkisov link starting with this pair. Depending on the type of singularity, our results point out that some of these weights do not work generically for a general member of the corresponding coarse moduli space of quartics. |
| title | Birational geometry of Calabi-Yau pairs $(\mathbb{P}^3, D)$ of coregularity 2 |
| topic | Algebraic Geometry 14E05, 14E07 (Primary) 14E30, 14J17, 14J30 (Secondary) |
| url | https://arxiv.org/abs/2402.13970 |