Non-tautological cycles on moduli spaces of smooth pointed curves

2024/10/06 by Dario Faro, Faro, Dario, Carolina Tamborini +1
Mathematics · #14C15 #14H10 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Mathematical Dynamics and Fractals #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2410.04400

openalex publication_date 2024/10/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 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 M_g,n for all but finitely many values of g and n.

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