Building on work of the fourth author and Morelli's work, we prove the weak factorization
conjecture for birational maps in characteristic zero: a birational map between complete …

We develop the theory of stratified toroidal varieties, which gives, together with the theory of
birational cobordisms [73], a proof of the weak factorization conjecture for birational maps in …

arXiv:math/0002084v1 [math.AG] 11 Feb 2000 Page 1 arXiv:math/0002084v1 [math.AG] 11
Feb 2000 LECTURES ON FACTORIZATION OF BIRATIONAL MAPS Kenji Matsuki in memory …

This paper classifies proper birational morphisms of smooth threefolds collapsing three
smooth surfaces meeting normally to a point. In addition to three blow-ups and Hironaka's …

THEOREM 1. Let T be an algebraic torus. Suppose that X is a normal variety isomorphic in
codimension one to a torus embedding-ie, X less a subset of codimen-sion at least two is …

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 …

Using combinatorial methods, we classify all birational morphisms blowing m≦ 5 divisors
down to a point. Those which do not factor through the blowing up of a point are treated in …

Zariski proved around 1944 that every birational morphism between smooth surfaces over a
field k is a composition of blowing-ups at closed points. Later, around 1966 Shafarevich …

The aim of this master's thesis is to understand [Cra83] and [CM83]. In these papers, we
consider a smooth variety X over C, such that (i) Either X is the domain of a proper birational …

We develop the theory of stratified toroidal varieties, which gives, together with the theory of
birational cobordisms [73], a proof of the weak factorization conjecture for birational maps in …