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.

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

References in corpus (8)

• On the tautological ring of $\M _g$
• Quantum Cohomology and Virasoro Algebra
• Virasoro constraints and the Chern classes of the Hodge bundle
• Combinatorial and algebro-geometric cohomology classes on the moduli spaces of curves
• Hodge integrals and degenerate contributions
• Stable maps and branch divisors
• The Chow Ring of the Non-Linear Grassmannian
• Mapping Class Groups and Moduli Spaces of Curves

Cited by in corpus (4)

• Three questions in Gromov-Witten theory
• The String Landscape, the Swampland, and the Missing Corner
• Relations on ${\overline{M}}_{g,n}$ via equivariant Gromov-Witten theory of ${\mathbb{P}}^1$
• Generating functions for intersection numbers on moduli spaces of curves