Polynomial relations among kappa classes on the moduli space of curves

TL;DR

This paper constructs universal polynomial relations among kappa classes on the moduli space of curves, proposing a conjecture about their vanishing behavior depending on genus and marked points.

Contribution

It introduces an infinite collection of universal polynomials in kappa classes on moduli spaces, independent of genus and marked points, and formulates a conjecture about their vanishing.

Findings

Construction of universal polynomial relations among kappa classes.

Proposal of a conjecture on the vanishing of these polynomials.

Framework for understanding relations in the cohomology of moduli spaces.

Abstract

We construct an infinite collection of universal -- independent of $(g,n)$ -- polynomials in the Miller-Morita-Mumford classes $\kappa_m\in H^{2m}( \overline{\cal M}_{g,n},\bq)$, 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 $n$.