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  • © 2004

K3 Projective Models in Scrolls

Part of the book series: Lecture Notes in Mathematics (LNM, volume 1842)

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Table of contents (13 chapters)

  1. Front Matter

    Pages I-VIII
  2. 1. Introduction

    • Trygve Johnsen, Andreas Leopold Knutsen
    Pages 1-14
  3. 2. Surfaces in Scrolls

    • Trygve Johnsen, Andreas Leopold Knutsen
    Pages 15-18
  4. 4. Two existence theorems

    • Trygve Johnsen, Andreas Leopold Knutsen
    Pages 31-33
  5. 5. The singular locus of the surface S’ and the scroll \(\mathcal{T}\)

    • Trygve Johnsen, Andreas Leopold Knutsen
    Pages 35-45
  6. 6. Postponed proofs

    • Trygve Johnsen, Andreas Leopold Knutsen
    Pages 47-57
  7. 7. Projective models in smooth scrolls

    • Trygve Johnsen, Andreas Leopold Knutsen
    Pages 59-61
  8. 8. Projective models in singular scrolls

    • Trygve Johnsen, Andreas Leopold Knutsen
    Pages 63-98
  9. 10. BN general and Clifford general K3 surfaces

    • Trygve Johnsen, Andreas Leopold Knutsen
    Pages 121-128
  10. 11. Projective models of K3 surfaces of low genus

    • Trygve Johnsen, Andreas Leopold Knutsen
    Pages 129-154
  11. 12. Some applications and open questions

    • Trygve Johnsen, Andreas Leopold Knutsen
    Pages 155-158
  12. References

    • Trygve Johnsen, Andreas Leopold Knutsen
    Pages 159-162
  13. Back Matter

    Pages 163-164

About this book

The exposition studies projective models of K3 surfaces whose hyperplane sections are non-Clifford general curves. These models are contained in rational normal scrolls. The exposition supplements standard descriptions of models of general K3 surfaces in projective spaces of low dimension, and leads to a classification of K3 surfaces in projective spaces of dimension at most 10. The authors bring further the ideas in Saint-Donat's classical article from 1974, lifting results from canonical curves to K3 surfaces and incorporating much of the Brill-Noether theory of curves and theory of syzygies developed in the mean time.

Keywords

  • Clifford index of curves
  • Dimension
  • K3 surfaces
  • projective models
  • rational normal scrolls
  • syzygies

Reviews

From the reviews:

"The aim of this book is to give a description of projective models of K3 surfaces. It is clearly written and presents a complete exposition on the subject. The proofs use a variety of important techniques in projective geometry. … A graduate student interested in projective algebraic geometry could find this book quite useful and inspiring." (Sandra Di Rocco, Mathematical Reviews, Issue 2005 g)

Bibliographic Information

  • Book Title: K3 Projective Models in Scrolls

  • Authors: Trygve Johnsen, Andreas Leopold Knutsen

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/b97183

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 2004

  • Softcover ISBN: 978-3-540-21505-9Published: 13 May 2004

  • eBook ISBN: 978-3-540-40898-7Published: 30 April 2004

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: VIII, 172

  • Topics: Algebraic Geometry

Buying options

eBook USD 34.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 49.95
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