Grundlehren der mathematischen Wissenschaften

Geometry of Algebraic Curves

Volume I

Authors: Arbarello, E., Cornalba, M., Griffiths, P., Harris, J.D.

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About this Textbook

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).

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)


Table of contents (8 chapters)

  • Preliminaries

    Arbarello, E. (et al.)

    Pages 1-60

  • Determinantal Varieties

    Arbarello, E. (et al.)

    Pages 61-106

  • Introduction to Special Divisors

    Arbarello, E. (et al.)

    Pages 107-152

  • The Varieties of Special Linear Series on a Curve

    Arbarello, E. (et al.)

    Pages 153-202

  • The Basic Results of the Brill-Noether Theory

    Arbarello, E. (et al.)

    Pages 203-224

Buy this book

eBook $89.00
price for USA (gross)
  • ISBN 978-1-4757-5323-3
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $119.00
price for USA
  • ISBN 978-0-387-90997-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $119.00
price for USA
  • ISBN 978-1-4419-2825-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Geometry of Algebraic Curves
Book Subtitle
Volume I
Authors
Series Title
Grundlehren der mathematischen Wissenschaften
Series Volume
267
Copyright
1985
Publisher
Springer-Verlag New York
Copyright Holder
Springer-Verlag New York
eBook ISBN
978-1-4757-5323-3
DOI
10.1007/978-1-4757-5323-3
Hardcover ISBN
978-0-387-90997-4
Softcover ISBN
978-1-4419-2825-2
Series ISSN
0072-7830
Edition Number
1
Number of Pages
XVI, 387
Topics