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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Greer et al. (2024) studied this question.
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