© 2004

Positivity in Algebraic Geometry I

Classical Setting: Line Bundles and Linear Series


Table of contents

  1. Front Matter
    Pages I-XVIII
  2. Notation and Conventions

    1. Robert Lazarsfeld
      Pages 1-2
  3. Ample Line Bundles and Linear Series

    1. Front Matter
      Pages 3-3
    2. Robert Lazarsfeld
      Pages 5-6
    3. Robert Lazarsfeld
      Pages 7-119
    4. Robert Lazarsfeld
      Pages 121-183
    5. Robert Lazarsfeld
      Pages 185-237
    6. Robert Lazarsfeld
      Pages 239-267
    7. Robert Lazarsfeld
      Pages 269-312
  4. Back Matter
    Pages 313-387

About this book


This two volume work on Positivity in Algebraic Geometry contains a contemporary account of a body of work in complex algebraic geometry loosely centered around the theme of positivity. Topics in Volume I include ample line bundles and linear series on a projective variety, the classical theorems of Lefschetz and Bertini and their modern outgrowths, vanishing theorems, and local positivity. Volume II begins with a survey of positivity for vector bundles, and moves on to a systematic development of the theory of multiplier ideals and their applications. A good deal of this material has not previously appeared in book form, and substantial parts are worked out here in detail for the first time. At least a third of the book is devoted to concrete examples, applications, and pointers to further developments.

Volume I is more elementary than Volume II, and, for the most part, it can be read without access to Volume II.


Algebraic Varieties Line Bundles Linear Series Multiplier Ideals Vanishing Theorems Vector Bundles

Authors and affiliations

  1. 1.Department of MathematicsUniversity of MichiganAnn ArborUSA

Bibliographic information

  • Book Title Positivity in Algebraic Geometry I
  • Book Subtitle Classical Setting: Line Bundles and Linear Series
  • Authors R.K. Lazarsfeld
  • Series Title Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics
  • DOI
  • Copyright Information Springer-Verlag Berlin Heidelberg 2004
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Hardcover ISBN 978-3-540-22533-1
  • Softcover ISBN 978-3-540-22528-7
  • eBook ISBN 978-3-642-18808-4
  • Series ISSN 0071-1136
  • Edition Number 1
  • Number of Pages XVIII, 387
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Algebraic Geometry
  • Buy this book on publisher's site
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