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arXiv · 2411.09910

Noether-Lefschetz cycles on the moduli space of abelian varieties

Aitor Iribar Lopez
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Abstract

The locus of non-simple abelian varieties in the moduli space of principally polarized abelian varieties gives rise to Noether-Lefschetz cycles. We study their intersection theoretic properties using the tautological projection constructed in [CMOP24], and show that projection defines a homomorphism when restricted to cycles supported on that locus. Using Hecke correspondences and the pullback by Torelli we prove that $[\mathcal {A}_1 \times \mathcal A_{g-1}]$ is not tautological in the sense of [vdG99] for $g=12$ and $g\geq 16$ even. We also explore the connections between Noether-Lefschetz cycles and the Gromov-Witten theory of a moving elliptic curve.

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Aitor Iribar Lopez. 2024-11-15. Noether-Lefschetz cycles on the moduli space of abelian varieties. https://arxiv.org/abs/2411.09910

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