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The Moduli Space of Curves

  • Conference proceedings
  • © 1995

Overview

Editors:
  1. Robbert H. Dijkgraaf

    1. Faculteit Wiskunde en Informatica, Universiteit van Amsterdam, Amsterdam, The Netherlands

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  2. Carel F. Faber

    1. Faculteit Wiskunde en Informatica, Universiteit van Amsterdam, Amsterdam, The Netherlands

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  3. Gerard B. M. Geer

    1. Faculteit Wiskunde en Informatica, Universiteit van Amsterdam, Amsterdam, The Netherlands

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

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Table of contents (20 papers)

  1. Front Matter

    Pages i-xii
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  2. Distribution of Rational Points and Kodaira Dimension of Fiber Products

    • Lucia Caporaso
    Pages 1-12

  3. How Many Rational Points Can a Curve Have?

    • Lucia Caporaso, Joe Harris, Barry Mazur
    Pages 13-31

  4. Quantum Cohomology of Rational Surfaces

    • Bruce Crauder, Rick Miranda
    Pages 33-80

  5. Quantum Intersection Rings

    • P. Di Francesco, C. Itzykson
    Pages 81-148

  6. Mirror Symmetry and Elliptic Curves

    • Robbert Dijkgraaf
    Pages 149-163

  7. A Generalized Jacobi Theta Function and Quasimodular Forms

    • Masanobu Kaneko, Don Zagier
    Pages 165-172

  8. Boundary behaviour of Hurwitz schemes

    • Torsten Ekedahl
    Pages 173-198

  9. Operads and Moduli Spaces of Genus 0 Riemann Surfaces

    • E. Getzler
    Pages 199-230

  10. Resolution of Diagonals and Moduli Spaces

    • Victor Ginzburg
    Pages 231-266

  11. The Chow Ring of the Moduli Space of Curves of Genus 5

    • E. Izadi
    Pages 267-303

  12. The Cohomology of Algebras Over Moduli Spaces

    • Takashi Kimura, Alexander A. Voronov
    Pages 305-334

  13. Enumeration of Rational Curves Via Torus Actions

    • Maxim Kontsevich
    Pages 335-368

  14. Cellular Decompositions of Compactified Moduli Spaces of Pointed Curves

    • Eduard Looijenga
    Pages 369-400

  15. Generating Functions in Algebraic Geometry and Sums Over Trees

    • Yu. I. Manin
    Pages 401-417

  16. Holomorphicity and Non-holomorphicity in N = 2 Supersymmetric Field Theories

    • Hirosi Ooguri
    Pages 419-426

  17. An Arithmetic Problem in Surface Geometry

    • R. C. Penner
    Pages 427-466

  18. An orbifold partition of \(\bar M_g^n\)

    • Martin Pikaart
    Pages 467-482

  19. Moduli of curves with non-abelian level structure

    • M. Pikaart, A. J. de Jong
    Pages 483-509

  20. Q-Structure of Conformal Field Theory with Gauge Symmetries

    • Kenji Ueno
    Pages 511-531
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Keywords

About this book

This generalization of geometry is bound to have wide­ spread repercussions for mathematics as well as physics. The unearthing of it will entail a new golden age in the interaction of mathematics and physics. E. Witten (1986) The idea that the moduli space Mg of curves of fixed genus 9 - that is, the algebraic variety that parametrizes all curves of genus 9 - is an intriguing object in its own right seems to have come slowly. Although the para­ meters or moduli of curves surface in Riemann's famous memoir on abelian functions (from 1857) and in work of Hurwitz and later were considered by the geometers of the Italian school, for a long time they attracted attention only in the special case 9 = 1, where they were studied in the framework of the theory of modular functions. The work of Grothendieck, who in the early sixties pointed the way towards the right approach, and the subsequent construction (in 1965) of the moduli space Mg by Mumford were the first foundational work, to be followed by the construction of a compactification Mg by Deligne and Mumford in 1969. The theorem of Harris and Mumford saying that for 9 sufficiently large the space Mg is of general type was the first big insight in its structure.

Editors and Affiliations

  • Faculteit Wiskunde en Informatica, Universiteit van Amsterdam, Amsterdam, The Netherlands

    Robbert H. Dijkgraaf, Carel F. Faber, Gerard B. M. Geer

Bibliographic Information

  • Book Title: The Moduli Space of Curves

  • Editors: Robbert H. Dijkgraaf, Carel F. Faber, Gerard B. M. Geer

  • Series Title: Progress in Mathematics

  • DOI: https://doi.org/10.1007/978-1-4612-4264-2

  • Publisher: Birkhäuser Boston, MA

  • eBook Packages: Springer Book Archive

  • Copyright Information: Birkhäuser Boston 1995

  • Hardcover ISBN: 978-0-8176-3784-2Published: 18 October 1995

  • Softcover ISBN: 978-1-4612-8714-8Published: 19 November 2011

  • eBook ISBN: 978-1-4612-4264-2Published: 06 December 2012

  • Series ISSN: 0743-1643

  • Series E-ISSN: 2296-505X

  • Edition Number: 1

  • Number of Pages: XII, 563

  • Topics: Algebra, Topology, Algebraic Topology, Algebraic Geometry

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