Polynomial Relations Among Kappa Classes on the Moduli Space of Curves

We construct an infinite collection of universal—independent of $(g,n)$—polynomials in the Miller–Morita–Mumford classes κ ₘ∈ H²ᵐ( M̄g,n,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.