On explicit birational geometry for minimal n-folds of canonical dimension n-1

Fuente: arXiv
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Autori principali: Chen, Meng, Esser, Louis, Wang, Chengxi
Natura: Preprint
Pubblicazione: 2022
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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