Multiplicity and invariants in birational geometry
Multiplicity and invariants in birational geometry
复制标题
双有理几何中的多重性和不变量
DOI：
10.1016/j.jalgebra.2016.11.027
复制
发表时间：
2017
影响因子：
0.9
通讯作者：
Kohsuke Shibata
中科院分区：
文献类型：
--
作者：
伊藤大貴,宮本寛子,望月慎一,櫻井和朗（分担執筆）;和田猛（監修）;Kohsuke Shibata;Kohsuke Shibata
点的多重性是判断奇异性好坏的基本不变量。它是在纯代数环境中引入的。另一方面，我们也可以将对数正则阈值和最小对数差值附加到奇异点上，这是在两种理论背景下引入的。在本文中，我们给出了局部完全交的奇异点的双分不变量的函数多重性的界。作为一个应用，我们得到了关于32维局部完全交的正则奇点多重性的Watanabe猜想的肯定答案。
The multiplicity of a point on a variety is a fundamental invariant to estimate how the singularity is bad. It is introduced in a purely algebraic context. On the other hand, we can also attach to the singularity the log canonical threshold and the minimal log discrepancy, which are introduced in a birational theoretic context. In this paper, we show bounds of the multiplicity by functions of these birational invariants for a singularity of locally a complete intersection. As an application, we obtain the affirmative answer to Watanabe's conjecture on the multiplicity of canonical singularity of locally a complete intersection up to dimension 32.