Polynomial Relations Among Kappa Classes on the Moduli Space of Curves

Abstract

Abstract We construct an infinite collection of universal—independent of $(g,n)$—polynomials in the Miller–Morita–Mumford classes $\kappa _m\in H^{2m}( \overline{\mathcal{M}}_{g,n},{\mathbb{Q}})$, defined over the moduli space of genus $g$ stable curves with $n$ labeled points. We conjecture vanishing of these polynomials in a range depending on $g$ and $n$.