Torification and Factorization of Birational Maps

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

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.
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

Keywords

Algebraic Geometry, Complex Variables, Differential Geometry, 14E05;14L30;14M25;58E05;57R90

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/78399

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/9904135
 http://arxiv.org/abs/math/9904135

Collections

arXiv