Volumes in Calabi-Yau Complete Intersection of Products of Projective Space
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866914007686840320 |
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| author | Tsai, Yi-Heng |
| author_facet | Tsai, Yi-Heng |
| contents | We prove that the birational automorphism group of a general Calabi-yau complete intersection $X$ given by ample divisors in $\mathbb{P}^{n_1}\times\cdots\times\mathbb{P}^{n_l}$ is always Lorentzain. Applying the Kawamata-Morrison cone theorem on such $X$, we compute $\operatorname{vol}_X(D+sA)$ for any divisor $D\in \partial\overline{\operatorname{Eff}}(X)$ and ample divisor $A$ when $s$ is small. We also provide examples of volumes of certain Cartier divisors that involve the digamma function. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_03949 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Volumes in Calabi-Yau Complete Intersection of Products of Projective Space Tsai, Yi-Heng Algebraic Geometry We prove that the birational automorphism group of a general Calabi-yau complete intersection $X$ given by ample divisors in $\mathbb{P}^{n_1}\times\cdots\times\mathbb{P}^{n_l}$ is always Lorentzain. Applying the Kawamata-Morrison cone theorem on such $X$, we compute $\operatorname{vol}_X(D+sA)$ for any divisor $D\in \partial\overline{\operatorname{Eff}}(X)$ and ample divisor $A$ when $s$ is small. We also provide examples of volumes of certain Cartier divisors that involve the digamma function. |
| title | Volumes in Calabi-Yau Complete Intersection of Products of Projective Space |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2503.03949 |