Logarithmic series and Hodge integrals in the tautological ring (with an appendix by D. Zagier)
Abstract
We describe a new perspective on the intersection theory of the moduli space of curves involving both Virasoro constraints and Gorenstein conditions. The main result of the paper is the computation of a basic 1-point Hodge integral series occurring in the tautological ring of the moduli space of nonsingular curves. In the appendix by D. Zagier, "Polynomials arising from the tautological ring", a detailed study is made of certain polynomials whose coefficients are intersection numbers on moduli space. The paper and the appendix together provide proofs of all previously conjectured formulas for 1-point integrals in the tautological ring, and of natural extensions of these formulas as well.
Keywords
Cite
@article{arxiv.math/0002112,
title = {Logarithmic series and Hodge integrals in the tautological ring (with an appendix by D. Zagier)},
author = {C. Faber and R. Pandharipande},
journal= {arXiv preprint arXiv:math/0002112},
year = {2007}
}
Comments
Minor changes. 26 pages, LaTeX2e. Appendix by D. Zagier: 12 pages, AmSTeX 2.1