© 1998

Algebraic Geometry III

Complex Algebraic Varieties Algebraic Curves and Their Jacobians

  • A. N. Parshin
  • I. R. Shafarevich

Part of the Encyclopaedia of Mathematical Sciences book series (EMS, volume 36)

Table of contents

  1. Front Matter
    Pages i-vii
  2. Vik. S. Kulikov, P. F. Kurchanov
    Pages 1-217
  3. V. V. Shokurov
    Pages 219-261
  4. Back Matter
    Pages 263-270

About this book


The first contribution of this EMS volume on the subject of complex algebraic geometry touches upon many of the central problems in this vast and very active area of current research. While it is much too short to provide complete coverage of this subject, it provides a succinct summary of the areas it covers, while providing in-depth coverage of certain very important fields - some examples of the fields treated in greater detail are theorems of Torelli type, K3 surfaces, variation of Hodge structures and degenerations of algebraic varieties.
The second part provides a brief and lucid introduction to the recent work on the interactions between the classical area of the geometry of complex algebraic curves and their Jacobian varieties, and partial differential equations of mathematical physics. The paper discusses the work of Mumford, Novikov, Krichever, and Shiota, and would be an excellent companion to the older classics on the subject by Mumford.


Algebraic curves Complex algebraic varieties Hodge structures Hodgesche Struktur Jacobian varieties Jacobischen Varietät Sätze von algebraic varieties algebraische Kurven differential equation komplexe algebraische Varietät mathematical physics

Authors and affiliations

  1. 1.Moscow State University of Transport Communications (MIIT)MoscowRussia
  2. 2.Department of MathematicsThe Johns Hopkins UniversityBaltimoreUSA

Editors and affiliations

  • A. N. Parshin
    • 1
  • I. R. Shafarevich
    • 1
  1. 1.Steklov Mathematical InstituteMoscowRussia

Bibliographic information

  • Book Title Algebraic Geometry III
  • Book Subtitle Complex Algebraic Varieties Algebraic Curves and Their Jacobians
  • Editors A.N. Parshin
    I.R. Shafarevich
  • Series Title Encyclopaedia of Mathematical Sciences
  • DOI
  • Copyright Information Springer-Verlag Berlin Heidelberg 1998
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Hardcover ISBN 978-3-540-54681-8
  • Softcover ISBN 978-3-642-08118-7
  • eBook ISBN 978-3-662-03662-4
  • Series ISSN 0938-0396
  • Edition Number 1
  • Number of Pages VIII, 270
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Additional Information Original Russian edition published by VINITI, Moscow, 1989
  • Topics Algebraic Geometry
    Number Theory
  • Buy this book on publisher's site