论文标题
功能分辨率除外。环形紧凑
Functorial resolution except for toroidal locus. Toroidal compactification
论文作者
论文摘要
令$ x $为特征零的任何种类。令$ v \子集X $为具有环形奇点的开放子集。我们显示了$ x $除外的规范降低的存在。此外，出色的除数在$ y $上具有简单的普通横梁。该定理自然会概括道型典型的降低。它不会修改非语言基因座$ v $，并将$ x $转换为非词性品种$ y $。尤其是Abramkin -temkin -wlodarczyk证明了对数品种的规范降低的证明使用。它还依靠此处建立的局部曲折品种的规范函数降低，并具有未修改的开放环形子集。作为一种应用，我们显示了环形摩环变种的环形方程压实的存在。这里的所有结果都可以链接到本文中开发的简单函数组合降低算法。
Let $X$ be any variety in characteristic zero. Let $V \subset X$ be an open subset that has toroidal singularities. We show the existence of a canonical desingularization of $X$ except for V. It is a morphism $f: Y \to X$ , which does not modify the subset $ V $ and transforms $X$ into a toroidal embedding $Y$, with singularities extending those on $V$. Moreover, the exceptional divisor has simple normal crossings on $Y$. The theorem naturally generalizes the Hironaka canonical desingularization. It does not modify the nonsingular locus $V$ and transforms $X$ into a nonsingular variety $Y$. The proof uses, in particular, the canonical desingularization of logarithmic varieties recently proved by Abramovich -Temkin-Wlodarczyk. It also relies on the established here canonical functorial desingularization of locally toric varieties with an unmodified open toroidal subset. As an application, we show the existence of a toroidal equisingular compactification of toroidal varieties. All the results here can be linked to a simple functorial combinatorial desingularization algorithm developed in this paper.
