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© 1985

Geometry of Algebraic Curves

Volume I

Textbook

Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 267)

Table of contents

  1. Front Matter
    Pages i-xvi
  2. E. Arbarello, M. Cornalba, P. A. Griffiths, J. Harris
    Pages 1-60
  3. E. Arbarello, M. Cornalba, P. A. Griffiths, J. Harris
    Pages 61-106
  4. E. Arbarello, M. Cornalba, P. A. Griffiths, J. Harris
    Pages 107-152
  5. E. Arbarello, M. Cornalba, P. A. Griffiths, J. Harris
    Pages 153-202
  6. E. Arbarello, M. Cornalba, P. A. Griffiths, J. Harris
    Pages 203-224
  7. E. Arbarello, M. Cornalba, P. A. Griffiths, J. Harris
    Pages 225-303
  8. E. Arbarello, M. Cornalba, P. A. Griffiths, J. Harris
    Pages 304-329
  9. E. Arbarello, M. Cornalba, P. A. Griffiths, J. Harris
    Pages 330-373
  10. Back Matter
    Pages 375-387

About this book

Introduction

In recent years there has been enormous activity in the theory of algebraic curves. Many long-standing problems have been solved using the general techniques developed in algebraic geometry during the 1950's and 1960's. Additionally, unexpected and deep connections between algebraic curves and differential equations have been uncovered, and these in turn shed light on other classical problems in curve theory. It seems fair to say that the theory of algebraic curves looks completely different now from how it appeared 15 years ago; in particular, our current state of knowledge repre­ sents a significant advance beyond the legacy left by the classical geometers such as Noether, Castelnuovo, Enriques, and Severi. These books give a presentation of one of the central areas of this recent activity; namely, the study of linear series on both a fixed curve (Volume I) and on a variable curve (Volume II). Our goal is to give a comprehensive and self-contained account of the extrinsic geometry of algebraic curves, which in our opinion constitutes the main geometric core of the recent advances in curve theory. Along the way we shall, of course, discuss appli­ cations of the theory of linear series to a number of classical topics (e.g., the geometry of the Riemann theta divisor) as well as to some of the current research (e.g., the Kodaira dimension of the moduli space of curves).

Keywords

Algebraic Curves Geometry algebra moduli space

Authors and affiliations

  1. 1.Dipartimento di Matematica, Istituto “Guido Castelnuovo”Università di Roma “La Sapienza”RomaItalia
  2. 2.Dipartimento di MatematicaUniversità di PaviaPaviaItalia
  3. 3.Office of the ProvostDuke UniversityDurhamUSA
  4. 4.Department of MathematicsBrown UniversityProvidenceUSA

Bibliographic information

  • Book Title Geometry of Algebraic Curves
  • Book Subtitle Volume I
  • Authors Enrico Arbarello
    Maurizio Cornalba
    Phillip Griffiths
    Joseph Daniel Harris
  • Series Title Grundlehren der mathematischen Wissenschaften
  • DOI https://doi.org/10.1007/978-1-4757-5323-3
  • Copyright Information Springer-Verlag New York 1985
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Hardcover ISBN 978-0-387-90997-4
  • Softcover ISBN 978-1-4419-2825-2
  • eBook ISBN 978-1-4757-5323-3
  • Series ISSN 0072-7830
  • Series E-ISSN 2196-9701
  • Edition Number 1
  • Number of Pages XVI, 387
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Algebraic Geometry
  • Buy this book on publisher's site
Industry Sectors
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Reviews

From the reviews:

“A comprehensive account of the deepest results of the geometry of algebraic curves that were obtained in the second half of the 20th century using some of the more advanced techniques of abstract algebraic geometry … . at the end of every chapter there bibliographical notes that guide the reader to the original literature and further developments and sets of exercises that complement the theory … . an immediate standard reference for researchers and students working on the geometry of algebraic curves … .” (Felipe Zaldivar, The Mathematical Association of America, July, 2011)