论文标题
关于最小的n倍n倍n-1的显式birational几何形状
On explicit birational geometry for minimal n-folds of canonical dimension n-1
论文作者
论文摘要
令$ n \ geq 2 $为任何整数。我们研究了规范量的最佳下限$ v_ {n，n-i} $，以及最小的投影性$ n $ folds typer类型的规范稳定性指数的最佳上限$ r_ {n，n-i} $，这些指数由$ i $ -folds（$ i $ -folds（$ i = 0,1 $ i = 0,1 $）构成典型的通用类型。 $ i = 0 $，$ v_ {n，n} = 2 $和$ r_ {n，n} = n+2 $的结果是专家已知的。在本文中，我们表明$ v_ {n，n-1} = \ frac {6} {2n+（n \ bmod 3）} $和$ r_ {n，n，n，n-1} = \ frac {1} {1} {3} {3}（5n+ 3+（n \ bmod 3））$。该机械适用于所有规范尺寸$ n-i $。
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 $n-i$.
