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Admissible covers and stable maps

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arxiv 2505.03487 v2 pith:AAQKJ4RG submitted 2025-05-06 math.AG

Denis Nesterov , Maximilian Schimpf , Johannes Schmitt This is my paper · ORCID
classification math.AG
keywords formulaadmissiblecoverscyclesmapsstablecasescomputationally
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abstract

Moduli spaces of admissible covers and stable maps of target curves give rise to cycles on $\overline{M}_{g,n}$. We prove a formula relating these cycles. It recovers both the Ekedahl-Lando-Shapiro-Vainshtein formula and the Gromov-Witten/Hurwitz correspondence, providing a cycle-theoretic refinement thereof. The formula is verified computationally in low-genus cases with the help of Johannes Schmitt.

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  1. Torelli loci, product cycles, and the homomorphism conjecture for $\mathcal{A}_g$

    math.AG 2026-01 conditional novelty 7.0 of 10

    For 2≤g≤8, taut([J_g]·[A_2×A_{g-2}]) = taut([J_g])·taut([A_2×A_{g-2}]), and similarly for ([J_6],[A_3×A_3]); the paper also constructs new Gorenstein-kernel classes in compact-type moduli spaces.

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