Toroidal varieties and the weak factorization theorem

• 成果类型: Article
• 署名作者: Wlodarczyk, J
• 署名单位: Purdue University System; Purdue University
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-003-0305-8
• 发表日期: 2003
• 页码: 223-331
• 关键词: geometric invariant-theory; collapsing 3 surfaces; birational morphisms; blowing-up; SINGULARITIES; threefolds; RESOLUTION; bundles; cone; MAPS

摘要

We develop the theory of stratified toroidal varieties, which gives, together with the theory of birational cobordisms [73], a proof of the weak factorization conjecture for birational maps in characteristic zero: a birational map between complete nonsingular varieties over an algebraically closed field K of characteristic zero is a composite of blow-ups and blow-downs with smooth centers.