A GIT proof of Włodarczyk's weighted factorization theorem

1999/04/26 by Yi Hu, Hu, Yi, Seán Keel +2
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #Algebraic and Geometric Analysis #FOS: Mathematics #Mathematics and Applications #Matrix Theory and Algorithms #math.AG

paper · pdf · doi:10.48550/arxiv.math/9904146

5 pages

arxiv created 1999/04/26 · openalex publication_date 1999/04/26 · arxiv updated 2009/11/30 · openalex created_date 2020/08/13 · openalex updated_date 2026/07/28

Abstract

We give a short proof of W\lodarczyk's theorem that any birational map between smooth projective varieties in characteristic zero is a composition of weighted blowups and blowdowns.

Related

• Torification and Factorization of Birational Maps
• Birational cobordisms and factorization of birational maps
• Lectures on Factorization of Birational Maps
• Simple Constructive Weak Factorization
• Toroidal varieties and the weak Factorization Theorem