论文标题
通过加权环形爆炸的对数分辨率
Logarithmic resolution via weighted toroidal blow-ups
论文作者
论文摘要
令$ x $是一种通常在对数上平滑的FS对数方案，并且在特征性零的字段$ \ kk $上，将严格的封闭嵌入到对数方案$ y $中。我们为$ x $的功能对数分辨率构建一个简单快速的过程，其中最终结果尤其是堆栈理论修改$ x'\ rightarrow x $，这样$ x'$在$ k $上是对数平滑的。特别是，如果$ x $是光滑的$ k $ -scheme $ y $的封闭式，则该过程不仅具有与阿布拉莫维奇 - 塞姆金 - 沃达克的“梦想解决方案算法”相同的理想功能Arxiv：1906.07106。结果，我们恢复了Hironaka在特征零中解决奇异性的一种不同，更简单的方法。
Let $X$ be a fs logarithmic scheme that is generically logarithmically smooth, and that admits a strict closed embedding into a logarithmically smooth scheme $Y$ over a field $\kk$ of characteristic zero. We construct a simple and fast procedure to functorial logarithmic resolution of $X$, where the end result is in particular a stack-theoretic modification $X' \rightarrow X$ such that $X'$ is logarithmically smooth over $k$. In particular, if $X$ is a closed subscheme of a smooth $k$-scheme $Y$, the procedure not only shares the same desirable features as the 'dream resolution algorithm' of Abramovich-Temkin-Wlodarczyk (arXiv:1906.07106), but also accounts for a key feature of Hironaka's Main Theorem I, which was not addressed in arXiv:1906.07106. As a consequence, we recover a different and simpler approach to Hironaka's resolution of singularities in characteristic zero.
