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Progress in Mathematics

The Moduli Space of Curves

Editors: Dijkgraaf, Robert H., Faber, Carel, Geer, Gerard B.M. van der (Eds.)

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About this book

The moduli space Mg of curves of fixed genus g – that is, the algebraic variety that parametrizes all curves of genus g – is one of the most intriguing objects of study in algebraic geometry these days. Its appeal results not only from its beautiful mathematical structure but also from recent developments in theoretical physics, in particular in conformal field theory.

Leading experts in the field explore in this volume both the structure of the moduli space of curves and its relationship with physics through quantum cohomology. Altogether, this is a lively volume that testifies to the ferment in the field and gives an excellent view of the state of the art for both mathematicians and theoretical physicists. It is a persuasive example of the famous Wignes comment, and its converse, on "the unreasonable effectiveness of mathematics in the natural science."

Witteen’s conjecture in 1990 describing the intersection behavior of tautological classes in the cohomology of Mg arose directly from string theory. Shortly thereafter a stunning proof was provided by Kontsevich who, in this volume, describes his solution to the problem of counting rational curves on certain algebraic varieties and includes numerous suggestions for further development. The same problem is given an elegant treatment in a paper by Manin. There follows a number of contributions to the geometry, cohomology, and arithmetic of the moduli spaces of curves. In addition, several contributors address quantum cohomology and conformal field theory.

Table of contents (20 chapters)

Table of contents (20 chapters)

Buy this book

eBook $169.00
price for USA in USD
  • ISBN 978-1-4612-4264-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $219.99
price for USA in USD
  • ISBN 978-0-8176-3784-2
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • Usually dispatched within 3 to 5 business days.
Softcover $219.99
price for USA in USD
  • ISBN 978-1-4612-8714-8
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
The Moduli Space of Curves
Editors
  • Robert H. Dijkgraaf
  • Carel Faber
  • Gerard B.M. van der Geer
Series Title
Progress in Mathematics
Series Volume
129
Copyright
1995
Publisher
Birkhäuser Basel
Copyright Holder
Birkhäuser Boston
eBook ISBN
978-1-4612-4264-2
DOI
10.1007/978-1-4612-4264-2
Hardcover ISBN
978-0-8176-3784-2
Softcover ISBN
978-1-4612-8714-8
Series ISSN
0743-1643
Edition Number
1
Number of Pages
XII, 563
Topics

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