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The Moduli Space of Curves

  • Robbert H. Dijkgraaf
  • Carel F. Faber
  • Gerard B. M. van der Geer

Part of the Progress in Mathematics book series (PM, volume 129)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Lucia Caporaso, Joe Harris, Barry Mazur
    Pages 13-31
  3. Bruce Crauder, Rick Miranda
    Pages 33-80
  4. P. Di Francesco, C. Itzykson
    Pages 81-148
  5. Robbert Dijkgraaf
    Pages 149-163
  6. Masanobu Kaneko, Don Zagier
    Pages 165-172
  7. Torsten Ekedahl
    Pages 173-198
  8. Victor Ginzburg
    Pages 231-266
  9. Takashi Kimura, Alexander A. Voronov
    Pages 305-334
  10. Maxim Kontsevich
    Pages 335-368
  11. R. C. Penner
    Pages 427-466
  12. Martin Pikaart
    Pages 467-482
  13. M. Pikaart, A. J. de Jong
    Pages 483-509

About these proceedings

Introduction

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.

Keywords

Arithmetic Cohomology Counting algebra algebraic geometry algebraic varieties function geometry mathematics moduli space proof theoretical physics

Editors and affiliations

  • Robbert H. Dijkgraaf
    • 1
  • Carel F. Faber
    • 1
  • Gerard B. M. van der Geer
    • 1
  1. 1.Faculteit Wiskunde en InformaticaUniversiteit van AmsterdamAmsterdamThe Netherlands

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-4264-2
  • Copyright Information Birkhäuser Boston 1995
  • Publisher Name Birkhäuser Boston
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-8714-8
  • Online ISBN 978-1-4612-4264-2
  • Series Print ISSN 0743-1643
  • Series Online ISSN 2296-505X
  • Buy this book on publisher's site