On explicit birational geometry for minimal n-folds of canonical dimension n-1
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866917594309591040 |
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| author | Chen, Meng Esser, Louis Wang, Chengxi |
| author_facet | Chen, Meng Esser, Louis Wang, Chengxi |
| contents | Let $n\geq 2$ be any integer. We study the optimal lower bound $v_{n, n-i}$ of the canonical volume and the optimal upper bound $r_{n,n-i}$ of the canonical stability index for minimal projective $n$-folds of general type, which are canonically fibered by $i$-folds ($i=0,1$). The results for $i = 0$, $v_{n,n}=2$ and $r_{n, n}=n+2$, are known to experts. In this article, we show that $v_{n,n-1}=\frac{6}{2n+(n \bmod 3)}$ and $r_{n,n-1}=\frac{1}{3}(5n+ 3 + (n \bmod 3))$. The machinery is applicable to all canonical dimensions $n-i$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2201_08966 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On explicit birational geometry for minimal n-folds of canonical dimension n-1 Chen, Meng Esser, Louis Wang, Chengxi Algebraic Geometry Complex Variables Let $n\geq 2$ be any integer. We study the optimal lower bound $v_{n, n-i}$ of the canonical volume and the optimal upper bound $r_{n,n-i}$ of the canonical stability index for minimal projective $n$-folds of general type, which are canonically fibered by $i$-folds ($i=0,1$). The results for $i = 0$, $v_{n,n}=2$ and $r_{n, n}=n+2$, are known to experts. In this article, we show that $v_{n,n-1}=\frac{6}{2n+(n \bmod 3)}$ and $r_{n,n-1}=\frac{1}{3}(5n+ 3 + (n \bmod 3))$. The machinery is applicable to all canonical dimensions $n-i$. |
| title | On explicit birational geometry for minimal n-folds of canonical dimension n-1 |
| topic | Algebraic Geometry Complex Variables |
| url | https://arxiv.org/abs/2201.08966 |