1999/04/15 by Jaroslaw Wlodarczyk, Wlodarczyk, Jaroslaw
Mathematics · #14E05 #14L30 #14M25 #57R90 #58E05 #Algebraic Geometry (math.AG) #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #math.AG #math.CV #math.DG #msc:14E05 #msc:14L30 #msc:14M25 #msc:57R90 #msc:58E05
paper · pdf · doi:10.48550/arxiv.math/9904076
69 pages, a revised version with conceptual simplifications. The present version is self-contained and it does not rely on weak factorization theorem for toric varieties
arxiv created 2002/07/25 · arxiv updated 2016/09/07
The main goal of the present paper is two-fold. First we extend the theory of toroidal embeddings introduced by Kempf, Knudsen, Mumford and Saint-Donat to the class of toroidal varieties with stratifications (which is the main body of the paper). Second we give a proof of the following weak factorization theorem as an application and illustration of the theory: 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. Another proof of the weak factorization theorem appeared in a joint paper with Abramovich, Karu and Matsuki (math.AG/9904135) In that paper the theorem is stated and proven in general for proper algebraic and analytic spaces.