Grundlehren der mathematischen Wissenschaften

Geometry of Algebraic Curves

Volume II with a contribution by Joseph Daniel Harris

Authors: Arbarello, Enrico, Cornalba, Maurizio, Griffiths, Phillip

  • Written by experts who have actively participated in the development of the Geometry of Algebraic Curves
  • Long expected second volume
  • As with the first volume (Grundlehren volume 267), it is expected that it will become the central reference work on this subject
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About this Textbook

The second volume of the Geometry of Algebraic Curves is devoted to the foundations of the theory of moduli of algebraic curves. Its authors are research mathematicians who have actively participated in the development of the Geometry of Algebraic Curves. The subject is an extremely fertile and active one, both within the mathematical community and at the interface with the theoretical physics community. The approach is unique in its blending of algebro-geometric, complex analytic and topological/combinatorial methods. It treats important topics such as Teichmüller theory, the cellular decomposition of moduli and its consequences and the Witten conjecture. The careful and comprehensive presentation of the material will be of value to students who wish to learn the subject and to experts as a reference source.

The first volume appeared 1985 as volume 267 of the same series.

Reviews

From the reviews:

“This second volume will become the standard reference for researchers and students working on the algebraic geometry of curves. With almost 700 items in the rich 42-page bibliography, bibliographical notes at the end of every chapter to guide the reader and sets of (guided) exercises as in the first volume, this second volume is an interactive resource for everyone seriously interested on this beautiful part of algebraic geometry. We owe the authors a heartfelt thank you for writing such a rich, beautiful and full treatise.” (Felipe Zaldivar, The Mathematical Association of America, July, 2011)

“Here, after a quarter of a century, is finally the sequel to Volume I … . That volume, essentially devoted to properties of a single curve … . The present volume has its focus on their moduli … . The book under review is very helpful for reference and for learning the details … . Summing up: every algebraic geometer should have a copy, while a Teichmüller person and a topologist should seriously consider getting one.” (E. Looijenga, Mathematical Reviews, Issue 2012 e)

“Provide comprehensive and detailed foundations for the theory of moduli of complex algebraic curves, and that from multiple perspectives and various points of view. … The bibliography at the end of the book is extremely rich and very up-to-date. … The current book is an excellent research monograph and reference book in the theory of complex algebraic curves and their moduli, which is very likely to become an indispensable source for researchers and graduate students in both complex geometry and mathematical physics.” (Werner Kleinert, Zentralblatt MATH, Vol. 1235, 2012)


Table of contents (13 chapters)

  • The Hilbert Scheme

    Arbarello, Enrico (et al.)

    Pages 1-77

  • Nodal curves

    Arbarello, Enrico (et al.)

    Pages 79-166

  • Elementary deformation theory and some applications

    Arbarello, Enrico (et al.)

    Pages 167-248

  • The moduli space of stable curves

    Arbarello, Enrico (et al.)

    Pages 249-328

  • Line bundles on moduli

    Arbarello, Enrico (et al.)

    Pages 329-397

Buy this book

eBook $89.00
price for USA
  • ISBN 978-3-540-69392-5
  • 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 978-3-540-42688-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Geometry of Algebraic Curves
Book Subtitle
Volume II with a contribution by Joseph Daniel Harris
Authors
Series Title
Grundlehren der mathematischen Wissenschaften
Series Volume
268
Copyright
2011
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-69392-5
DOI
10.1007/978-3-540-69392-5
Hardcover ISBN
978-3-540-42688-2
Series ISSN
0072-7830
Edition Number
1
Number of Pages
XXX, 963
Topics