On numerical dimensions of Calabi--Yau varieties
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866911886338949120 |
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| author | Jiang, Chen Wang, Long |
| author_facet | Jiang, Chen Wang, Long |
| contents | Let $X$ be a Calabi--Yau variety of Picard number two with infinite birational automorphism group. We show that the numerical dimension $κ^{\mathbb{R}}_σ$ of the extremal rays of the closed movable cone of $X$ is $\dim X/2$. More generally, we investigate the relation between the two numerical dimensions $κ^{\mathbb{R}}_σ$ and $κ^{\mathbb{R}}_{\mathrm{vol}}$ for Calabi--Yau varieties. We also compute $κ^{\mathbb{R}}_σ$ for non-big divisors in the closed movable cone of a projective hyperkähler manifold. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_00654 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On numerical dimensions of Calabi--Yau varieties Jiang, Chen Wang, Long Algebraic Geometry Let $X$ be a Calabi--Yau variety of Picard number two with infinite birational automorphism group. We show that the numerical dimension $κ^{\mathbb{R}}_σ$ of the extremal rays of the closed movable cone of $X$ is $\dim X/2$. More generally, we investigate the relation between the two numerical dimensions $κ^{\mathbb{R}}_σ$ and $κ^{\mathbb{R}}_{\mathrm{vol}}$ for Calabi--Yau varieties. We also compute $κ^{\mathbb{R}}_σ$ for non-big divisors in the closed movable cone of a projective hyperkähler manifold. |
| title | On numerical dimensions of Calabi--Yau varieties |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2208.00654 |