Nontautological cycles on moduli spaces of smooth pointed curves

Abstract

In recent work by Arena, Canning, Clader, Haburcak, Li, Mok, and Tamborini, it was proven that for infinitely many values of $g$ and $n$, there exist nontautological algebraic cohomology classes on the moduli space $M_{g,n}$ of smooth genus $g$, $n$-pointed curves. Here we show how a generalization of their technique allows to cover most of the remaining cases, proving the existence of nontautological algebraic cohomology classes on the moduli space $M_{g,n}$ for all but finitely many values of $g$ and $n$.