Memoirs of the American Mathematical Society 2007; 222 pp; softcover Volume: 190 ISBN10: 0821839985 ISBN13: 9780821839980 List Price: US$78 Individual Members: US$46.80 Institutional Members: US$62.40 Order Code: MEMO/190/890
 This book contains a proof that a dominant morphism from a 3fold \(X\) to a variety \(Y\) can be made toroidal by blowing up in the target and domain. We give applications to factorization of birational morphisms of 3folds. Table of Contents  Introduction
 An outline of the proof
 Notation
 Toroidal morphisms and prepared morphisms
 Toroidal ideals
 Toroidalization of morphisms from 3folds to surfaces
 Preparation above 2 and 3points
 Preparation
 The \(\tau\) invariant
 Super parameters
 Good and perfect points
 Relations
 Well prepared morphisms
 Construction of \(\tau\)well prepared diagrams
 Construction of a \(\tau\)very well prepared morphism
 Toroidalization
 Proofs of the main results
 List of technical terms
 Bibliography
