Torification and Factorization of Birational Maps
摘要
Building on the work of the fourth author in math.AG/9904074, we prove 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 blowings up and blowings down with smooth centers. Such a factorization exists which is functorial with respect to absolute isomorphisms, and compatible with a normal crossings divisor. The same holds for algebraic and analytic spaces. Another proof of the main theorem by the fourth author appeared in math.AG/9904076.
引用
@article{arxiv.math/9904135,
title = {Torification and Factorization of Birational Maps},
author = {Dan Abramovich and Kalle Karu and Kenji Matsuki and Jarosław Włodarczyk},
journal= {arXiv preprint arXiv:math/9904135},
year = {2007}
}
备注
The previous versions of this paper used Morelli's algorithm for strong factorization of toric birational maps, in which a gap was recently found by K. Karu. In this version we rely only on weak factorization of toric birational maps (due to Wlodarczyk and Morelli). The results remain the same