Discreteness of volumes of divisors on Calabi-Yau type varieties
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911095412752384 |
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| author | Jiao, Junpeng |
| author_facet | Jiao, Junpeng |
| contents | We study the volumes of divisors in Calabi--Yau type varieties. We show that given a klt Calabi--Yau pair $(X,B)$ and an integral divisor $A$ on $X$, the volume of $A$ is in a fixed discrete set depending only on the dimension and singularities of $(X,B)$. As an application, we prove a boundedness result of polarized log Calabi--Yau pairs which was conjectured by Birkar. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_05082 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Discreteness of volumes of divisors on Calabi-Yau type varieties Jiao, Junpeng Algebraic Geometry We study the volumes of divisors in Calabi--Yau type varieties. We show that given a klt Calabi--Yau pair $(X,B)$ and an integral divisor $A$ on $X$, the volume of $A$ is in a fixed discrete set depending only on the dimension and singularities of $(X,B)$. As an application, we prove a boundedness result of polarized log Calabi--Yau pairs which was conjectured by Birkar. |
| title | Discreteness of volumes of divisors on Calabi-Yau type varieties |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2508.05082 |