Abstract
Moduli spaces of compact stablen-pointed curves carry a hierarchy of cohomology classes of top dimension which generalize the Weil-Petersson volume forms and constitute a version of Mumford classes. We give various new formulas for the integrals of these forms and their generating functions.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
[AC] Arbarello, E., Cornalba, M.: Combinatorial and algebro-geometric cohomology classes on the moduli spaces of curves. Preprint, 1995 (to appear in J. of Alg. Geom).
[G] Getzler, E.: Operads and moduli spaces of genus zero Riemann surfaces In: The Moduli Space of Curves, ed. by R. Dijkgraaf, C. Faber, G. van der Geer, Progress in Math. vol.129, Basel-Boston; Birkhäuser, 1995, pp. 199–230
[Ke] Keel, S.: Intersection theory of moduli spaces of stablen-pointed curves of genus zero. Trans. AMS330, 545–574 (1992)
[K1] Kontsevich, M.: Intersection theory on the moduli space of curves and the matrix Airy function. Commun. Math. Phys.147, 1–23 (1992)
[K2] Kontsevich, M.: Enumeration of rational curves via torus actions. In: The Moduli Space of Curves, ed. by R. Dijkgraaf, C. Faber, G. van der Geer, Progress in Math. vol.129, Basel-Boston; Birkhäuser, 1995, pp. 335–368
[KM] Kontsevich, M., Yu. Manin.: Gromov-Witten classes, quantum cohomology, and enumerative geometry. Commun. Math. Phys.164:3, 525–562 (1994)
[KMK] Kontsevich, M., Yu. Manin (with Appendix by R. Kaufmann): Quantum cohomology of a product. Inv. Math.124, f. 1–3, 313–340 (1996)
[LS] Logan, B., Shepp, L.: A variational problem for random Young tableaux. Adv. in Math.26, (1977) 206–222
[M] Yu. Manin.: Generating functions in algebraic geometry and sums over trees. In: The Moduli Space of Curves, ed. by R. Dijkgraaf, C. Faber, G. van der Geer, Progress in Math., vol.129, Basel-Boston; Birkhäuser, 1995, pp. 401–418.
[Ma] Matone, M.: Nonperturbative model of Liouville gravity. Preprint hep-th/9402081
[W] Witten, E.: Two-dimensional gravity and intersection theory on moduli space. Surv. in Diff. Geo.1, 243–310 (1991)
[VK] A. Vershik, S. Kerov: Asymptotic theory of the characters of the symmetric group. Func. An. Appl.15:4, 15–27 (1981)
[Z] Zograf, P.: The Weil-Petersson volume of the moduli spaces of punctured spheres. In: Cont. Math. 150 (1993), ed. by R.M. Hain and C.F. Bödigheimer, pp. 267–372
Author information
Authors and Affiliations
Additional information
Communicated by A. Jaffe
Dedicated to the memory of Claude Itzykson
Rights and permissions
About this article
Cite this article
Kaufmann, R., Manin, Y. & Zagier, D. Higher Weil-Petersson volumes of moduli spaces of stablen-pointed curves. Commun.Math. Phys. 181, 763–787 (1996). https://doi.org/10.1007/BF02101297
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF02101297