Skip to main content
  • Book
  • © 2002

Monomialization of Morphisms from 3-Folds to Surfaces

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

Buying options

eBook USD 39.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 52.00
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

This is a preview of subscription content, access via your institution.

Table of contents (21 chapters)

  1. Front Matter

    Pages N2-V
  2. 1. Introduction

    • Steven Dale Cutkosky
    Pages 1-8
  3. 2. Local Monomialization

    • Steven Dale Cutkosky
    Pages 9-10
  4. 3. Monomialization of Morphisms in Low Dimensions

    • Steven Dale Cutkosky
    Pages 11-13
  5. 5. Notations

    • Steven Dale Cutkosky
    Pages 19-19
  6. 6. The Invariant \(\nu\)

    • Steven Dale Cutkosky
    Pages 20-55
  7. 7. The Invariant \(\nu\) Under Quadratic Transforms

    • Steven Dale Cutkosky
    Pages 56-76
  8. 9. Power Series in 2 Variables

    • Steven Dale Cutkosky
    Pages 93-108
  9. 10. \(\bf {A_r(X)}\)

    • Steven Dale Cutkosky
    Pages 109-109
  10. 11. Reduction of \(\nu\) in a Special Case

    • Steven Dale Cutkosky
    Pages 110-130
  11. 12. Reduction of \(\nu\) in a Second Special Case

    • Steven Dale Cutkosky
    Pages 131-149
  12. 13. Resolution 1

    • Steven Dale Cutkosky
    Pages 150-162
  13. 14. Resolution 2

    • Steven Dale Cutkosky
    Pages 163-175
  14. 15. Resolution 3

    • Steven Dale Cutkosky
    Pages 176-184
  15. 16. Resolution 4

    • Steven Dale Cutkosky
    Pages 185-187
  16. 17. Proof of the Main Theorem

    • Steven Dale Cutkosky
    Pages 188-188
  17. 18. Monomialization

    • Steven Dale Cutkosky
    Pages 189-223
  18. 19. Toroidalization

    • Steven Dale Cutkosky
    Pages 224-231

About this book

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

  • Book Title: Monomialization of Morphisms from 3-Folds to Surfaces

  • Authors: Steven Dale Cutkosky

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/b83848

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 2002

  • Softcover ISBN: 978-3-540-43780-2Published: 06 August 2002

  • eBook ISBN: 978-3-540-48030-3Published: 13 October 2004

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: VIII, 240

  • Topics: Algebraic Geometry

Buying options

eBook USD 39.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 52.00
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions