Mathematics – Algebraic Geometry
Scientific paper
1999-04-15
Mathematics
Algebraic Geometry
69 pages, a revised version with conceptual simplifications. The present version is self-contained and it does not rely on wea
Scientific paper
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.
No associations
LandOfFree
Toroidal varieties and the weak Factorization Theorem does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Toroidal varieties and the weak Factorization Theorem, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Toroidal varieties and the weak Factorization Theorem will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-145195