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Toroidalization of Dominant Morphisms of 3-Folds
Steven Dale Cutkosky, University of Missouri, Columbia, MO

Memoirs of the American Mathematical Society
2007; 222 pp; softcover
Volume: 190
ISBN-10: 0-8218-3998-5
ISBN-13: 978-0-8218-3998-0
List Price: US$82
Individual Members: US$49.20
Institutional Members: US$65.60
Order Code: MEMO/190/890
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This book contains a proof that a dominant morphism from a 3-fold \(X\) 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 3-folds.

Table of Contents

  • Introduction
  • An outline of the proof
  • Notation
  • Toroidal morphisms and prepared morphisms
  • Toroidal ideals
  • Toroidalization of morphisms from 3-folds to surfaces
  • Preparation above 2 and 3-points
  • 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
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