Canonical desingularization in characteristic zero by blowing up the maximum strata of a local invariant

• 成果类型: Article
• 署名作者: Bierstone, E; Milman, PD
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s002220050141
• 发表日期: 1997
• 页码: 207-302
• 关键词: analytic-functions

摘要

This article contains an elementary constructive proof of resolution of singularities in characteristic zero, Our proof al,plies in particular to schemes of finite type and to analytic spaces (so we recover the great theorems of Hironaka), We introduce a discrete local invariant inv(X)(a) whose maximum locus determines a smooth centre of blowing up, leading to desingularization, To define inv(X), we need only to work with a category of local-ringed spaces X = (/X/, C-X) satisfying certain natural conditions, If a epsilon /X/, then inv(X)(a) depends only on (C) over cap(X,a). More generally, inv(X) 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 inv(X)(.). 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.