Advertisement

Counting Riemann Surfaces

  • Bertrand Eynard
Chapter
Part of the Progress in Mathematical Physics book series (PMP, volume 70)

Abstract

In the previous chapter, we have computed the asymptotic generating functions of large maps, and we have seen that they are related to the ( p, q) minimal model.

Keywords

Modulus Space Riemann Surface Line Bundle Nodal Point Marked Point 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Bibliography

  1. 6.
    E. Arbarello, M. Cornalba, Combinatorial and algebro-geometric cohomology classes on the moduli space of curves. J. Algebraic Geom. 5, 705–709 (1996)MathSciNetzbMATHGoogle Scholar
  2. 7.
    E. Arbarello, J.D. Harris, M. Cornalba, P. Griffiths, Geometry of Algebraic Curves: Volume II with a Contribution by Joseph Daniel Harris, vol. 268 (Springer, New York, 2011)zbMATHGoogle Scholar
  3. 21.
    K.M. Chapman, M. Mulase, B. Safnuk, The Kontsevich constants for the volume of the moduli of curves and topological recursion. arXiv preprint (2010). arXiv:1009.2055Google Scholar
  4. 29.
    T. Ekedahl, S. Lando, M. Shapiro, A. Vainshtein, On Hurwitz numbers and Hodge integrals. C. R. Acad. Sci. Ser. I Math. 328(12), 1175–1180 (1999)MathSciNetzbMATHGoogle Scholar
  5. 45.
    J. Harer, D. Zagier, The euler characteristic of the moduli space of curves. Invent. Math. 85(3), 457–485 (1986)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 57.
    M. Kontsevich, Intersection theory on the moduli space of curves and the matrix airy function. Commun. Math. Phys. 147(1), 1–23 (1992)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 62.
    E. Looijenga, Cellular decompositions of compactified moduli spaces of pointed curves, in The Moduli Space of Curves (Springer, New York, 1995), pp. 369–400zbMATHGoogle Scholar
  8. 65.
    M. Mirzakhani, Simple geodesics and Weil-Petersson volumes of moduli spaces of bordered Riemann surfaces. Invent. Math. 167(1), 179–222 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 67.
    M. Mulase, B. Safnuk, Mirzakhani’s recursion relations, Virasoro constraints and the KdV hierarchy (2006), p. 21. arXiv:math/0601194Google Scholar
  10. 69.
    A. Okounkov, Generating functions for intersection numbers on moduli spaces of curves. Int. Math. Res. Not. 2002(18), 933–957 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 71.
    A. Okounkov, R. Pandharipande, Gromov-Witten theory, Hurwitz numbers, and matrix models, in I, Proc. Symposia Pure Math, vol. 80 (2009), pp. 325–414Google Scholar
  12. 75.
    R.C. Penner, Perturbative series and the moduli space of riemann surfaces. J. Differ. Geom. 27(1), 35–53 (1988)MathSciNetzbMATHGoogle Scholar
  13. 80.
    K. Strebel, Quadratic Differentials (Springer, New York, 1984)CrossRefzbMATHGoogle Scholar
  14. 87.
    E. Witten, Two dimensional gravity and intersection theory on moduli space. Surv. Differ. Geom. 1, 243–310 (1991)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 88.
    S. Wolpert, On the homology of the moduli space of stable curves. Ann. Math. 118(3), 491–523 (1983)MathSciNetCrossRefzbMATHGoogle Scholar
  16. 89.
    D. Zvonkine, Strebel differentials on stable curves and Kontsevich’s proof of Witten’s conjecture. arXiv preprint math/0209071 (2002)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Bertrand Eynard
    • 1
  1. 1.CEA Saclay Institut de Physique Théorique (IPHT)Gif sur YvetteFrance

Personalised recommendations