Products of boundary classes on M¯0,n via balanced weights

Abstract

In this note, we give a simple closed formula for an arbitrary product, landing in dimension 0, of boundary classes on the Deligne–Mumford moduli space ${\overline{M}}_{0,n}$. For any such boundary strata $X_{T_1},\dots ,X_{T_{\ell }}$, we show the intersection product $\int {\prod }_{i=1}^{\ell }\left[X_{T_i}\right]$ is either a signed product of multinomial coefficients, or zero, and provide a simple criterion for determining when it is nonzero.

We do not claim originality for our product formula, but to our knowledge it does not appear elsewhere in the literature.