Noether-Lefschetz cycles on the moduli space of abelian varieties
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866908668644032512 |
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| author | Lopez, Aitor Iribar |
| author_facet | Lopez, Aitor Iribar |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_09910 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Noether-Lefschetz cycles on the moduli space of abelian varieties Lopez, Aitor Iribar Algebraic Geometry 14K10 (Primary) 14C17 (Secondary) 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. |
| title | Noether-Lefschetz cycles on the moduli space of abelian varieties |
| topic | Algebraic Geometry 14K10 (Primary) 14C17 (Secondary) |
| url | https://arxiv.org/abs/2411.09910 |