Noether-Lefschetz cycles on the moduli space of abelian varieties

2024/11/15 by Lopez, Aitor Iribar · 1 citation
#14K10 (Primary) 14C17 (Secondary) #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2411.09910

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 A₁ × \mathcal A_g-1] is not tautological in the sense of [vdG99] for g=12 and g≥ 16 even. We also explore the connections between Noether-Lefschetz cycles and the Gromov-Witten theory of a moving elliptic curve.

Cited by

• Gromov-Witten theory of Hilbⁿ(ℂ²) and Noether-Lefschetz theory of A_g

Related

• Tautological and non-tautological cycles on the moduli space of abelian varieties
• Tautological projection for cycles on the moduli space of abelian varieties
• Cycles on the Moduli Space of Abelian Varieties
• Cycles on curves and Jacobians: a tale of two tautological rings
• Gromov-Witten theory of Hilbⁿ(ℂ²) and Noether-Lefschetz theory of A_g