论文标题
通过超级副本的乘数理想表征
A characterization of multiplier ideals via ultraproducts
论文作者
论文摘要
在本文中，使用Ultra-Frobenii，我们介绍了Schoutens的非标准紧密闭合，超紧密闭合的变体，这是本地域$ r $的理想，本质上是$ \ mathbb {c} $的有限类型的理想。我们证明，超测试的理想$τ_{\ rm u}（r，\ m athfrak {a}^t）$，$ r $的所有超紧密闭合关系的nihihilator理想，与乘数$ \ \ \ m nructer $ \ m nrucation $ $ \ mathcal $ \ mathcal profiel $ \ nrucation $ rathorname $ nistrage $ ragatigrak $ iS $ iS $ $ \ mathbb {q} $ - Gorenstein。作为应用，我们研究了纯环扩展条件下乘数理想的行为。
In this paper, using ultra-Frobenii, we introduce a variant of Schoutens' non-standard tight closure, ultra-tight closure, on ideals of a local domain $R$ essentially of finite type over $\mathbb{C}$. We prove that the ultra-test ideal $τ_{\rm u}(R,\mathfrak{a}^t)$, the annihilator ideal of all ultra-tight closure relations of $R$, coincides with the multiplier ideal $\mathcal{J}(\operatorname{Spec} R,\mathfrak{a}^t)$ if $R$ is normal $\mathbb{Q}$-Gorenstein. As an application, we study a behavior of multiplier ideals under pure ring extensions.
