Non-tautological cycles on moduli spaces of smooth pointed curves

Dario Faro; Carolina Tamborini

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arXiv · 2410.04400

Non-tautological cycles on moduli spaces of smooth pointed curves

Dario Faro·Carolina Tamborini

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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 non-tautological algebraic cohomology classes on the moduli space $\mathcal{M}_{g,n}$ 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 non-tautological algebraic cohomology classes on the moduli space $\mathcal{M}_{g,n}$ for all but finitely many values of $g$ and $n$.

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Dario Faro, Carolina Tamborini. 2024-10-06. Non-tautological cycles on moduli spaces of smooth pointed curves. https://arxiv.org/abs/2410.04400

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