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Monomialization of Morphisms from 3-folds to Surfaces

  • Authors
  • Steven┬áDale┬áCutkosky

Part of the Lecture Notes in Mathematics book series (LNM, volume 1786)

Table of contents

  1. Front Matter
    Pages N2-V
  2. Steven Dale Cutkosky
    Pages 1-8
  3. Steven Dale Cutkosky
    Pages 9-10
  4. Steven Dale Cutkosky
    Pages 11-13
  5. Steven Dale Cutkosky
    Pages 19-19
  6. Steven Dale Cutkosky
    Pages 20-55
  7. Steven Dale Cutkosky
    Pages 56-76
  8. Steven Dale Cutkosky
    Pages 93-108
  9. Steven Dale Cutkosky
    Pages 109-109
  10. Steven Dale Cutkosky
    Pages 110-130
  11. Steven Dale Cutkosky
    Pages 131-149
  12. Steven Dale Cutkosky
    Pages 150-162
  13. Steven Dale Cutkosky
    Pages 163-175
  14. Steven Dale Cutkosky
    Pages 176-184
  15. Steven Dale Cutkosky
    Pages 185-187
  16. Steven Dale Cutkosky
    Pages 188-188
  17. Steven Dale Cutkosky
    Pages 189-223
  18. Steven Dale Cutkosky
    Pages 224-231
  19. Steven Dale Cutkosky
    Pages 232-233
  20. Steven Dale Cutkosky
    Pages 234-235
  21. Back Matter
    Pages 237-239

About this book

Introduction

A morphism of algebraic varieties (over a field characteristic 0) is monomial if it can locally be represented in e'tale neighborhoods by a pure monomial mappings. The book gives proof that a dominant morphism from a nonsingular 3-fold X to a surface S can be monomialized by performing sequences of blowups of nonsingular subvarieties of X and S.
The construction is very explicit and uses techniques from resolution of singularities. A research monograph in algebraic geometry, it addresses researchers and graduate students.

Keywords

Algebraic Variety Monomialization Morphism Resolution of Singularities algebra algebraic varieties

Bibliographic information

  • DOI https://doi.org/10.1007/b83848
  • Copyright Information Springer-Verlag Berlin Heidelberg 2002
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-43780-2
  • Online ISBN 978-3-540-48030-3
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site