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$d$-elliptic loci and the Torelli map

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arxiv 2404.10826 v3 pith:ZIIAD632 submitted 2024-04-16 math.AG

François Greer , Carl Lian This is my paper · ORCID
classification math.AG
keywords ellipticcycletorelliabelianadmittingagreeclassclasses
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We show that two natural cycle classes on the moduli space of compact type stable maps to a varying elliptic curve agree. The first is the virtual fundamental class from Gromov-Witten theory, and the second is the Torelli pullback of the special cycle on A_g of principally polarized abelian varieties admitting an elliptic isogeny factor.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Gromov-Witten theory of $\mathsf{Hilb}^n(\mathbb{C}^2)$ and Noether-Lefschetz theory of $\mathcal{A}_g$

    math.AG 2025-06 conditional novelty 8.0 of 10

    The genus 1 divisor Gromov-Witten invariant of Hilb^n(C^2) is expressed through traces of quantum multiplication and equals the Eisenstein generating function that also governs Noether-Lefschetz cycles on A_g.

  2. 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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