Canonical desingularization in characteristic zero by blowing up the maximum strata of a local invariant
Canonical desingularization in characteristic zero by blowing up the maximum strata of a local invariant
复制标题
DOI：
10.1007/s002220050141
复制
发表时间：
1995-08
影响因子：
3.1
通讯作者：
E. Bierstone
中科院分区：
文献类型：
--
作者：
E. Bierstone
本文给出了特征零点奇点分解的一个初等构造性证明。我们的证明特别适用于计划的有限型和解析空间（所以我们恢复伟大的定理Hironaka）。我们引入了一个离散的局部不变量，其最大轨迹确定了一个光滑的中心爆破，导致去奇异化。为了定义，我们只需要处理一类满足一定自然条件的局部环形空间。如果，则只依赖于。更一般地，在任何爆破序列之后，其中心关于例外因子只有正常交叉并且位于的常轨迹中，归纳地定义。该文件是自成一体的，包括详细的例子。我们的目标之一是让读者理解去奇异化定理，而不是简单地“知道”它是真的。
This article contains an elementary constructive proof of resolution of singularities in characteristic zero. Our proof applies in particular to schemes of finite type and to analytic spaces (so we recover the great theorems of Hironaka). We introduce a discrete local invariantwhose maximum locus determines a smooth centre of blowing up, leading to desingularization. To define, we need only to work with a category of local-ringed spacessatisfying certain natural conditions. If, thendepends only on. More generally,is defined inductively after any sequence of blowings-up whose centres have only normal crossings with respect to the exceptional divisors and lie in the constant loci of. The paper is self-contained and includes detailed examples. One of our goals is that the reader understand the desingularization theorem, rather than simply “know” it is true.