Logarithmic series and Hodge integrals in the tautological ring (with an appendix by D. Zagier)

2000/02/14 by C. Faber, Faber, C., R. Pandharipande +1
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG

paper · pdf · doi:10.48550/arxiv.math/0002112

Minor changes. 26 pages, LaTeX2e. Appendix by D. Zagier: 12 pages, AmSTeX 2.1

arxiv created 2000/03/09 · arxiv updated 2009/11/30

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.

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