  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.
