论文标题
通过圆环动作的功能分辨率
Functorial resolution by torus actions
论文作者
论文摘要
我们提出了一种简单而快速的嵌入式分辨率，并使用对环境平滑品种（SNC）除外的环境平滑品种（SNC）分隔的环境动作进行了理想的原理化。特征零中的规范函数分辨率是通过沿平滑加权中心的新引入的爆炸来实现的。这些中心是由几何不变式定义的，该几何不变，以SNC除数测量平滑方案上的奇异性。输出是一种光滑的品种，具有圆环动作和SNC出色的除数。它的几何商对已解决的品种具有生物性，只有Abelian商的奇异性，并且可以通过纯粹的组合方法来塑造。该方法植根于与Abramovich和Temkin的联合工作中的想法，并且通过堆栈理论加权爆破与McQuillan的分辨率密切相关。作为一种应用，我们在正面和混合特征中为某些类别的奇点建立了分辨率结果。本文是早期预印本的缩短和修订版。
We present a simple and fast embedded resolution of varieties and principalization of ideals using torus actions on ambient smooth varieties with simple normal crossings (SNC) divisors. The canonical functorial resolution in characteristic zero is achieved via the newly introduced cobordant blow-ups along smooth weighted centers. These centers are defined by a geometric invariant measuring the singularities on smooth schemes with SNC divisors. The output is a smooth variety with a torus action and an SNC exceptional divisor. Its geometric quotient is birational to the resolved variety, has only abelian quotient singularities, and can be desingularized by purely combinatorial methods. The method is rooted in ideas from the joint work with Abramovich and Temkin and is closely related to McQuillan's resolution via stack-theoretic weighted blow-ups. As an application, we establish resolution results for certain classes of singularities in positive and mixed characteristic. This paper is a shortened and revised version of an earlier preprint.
