Intersections of 𝜓-classes on \overline{𝑀}_{1,𝑛}(𝑚)

We explain how to compute top-dimensional intersections of ψ \psi -classes on M ¯ 1 , n ( m ) \overline {M}_{1,n}(m) , the moduli space of m m -stable curves. On the spaces M ¯ 1 , n \overline {M}_{1,n} , these intersection numbers are determined by two recursions, namely, the string equation and dilaton equation. We establish, for each fixed m ≥ 1 m \geq 1 , an analogous pair of recursions that determine these intersection numbers on the spaces M ¯ 1 , n ( m ) \overline {M}_{1,n}(m) .