d-elliptic loci and the Torelli map

2024/04/16 by François Greer, Greer, François, Carl Lian +1 · 1 citation
Mathematics · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #FOS: Mathematics #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2404.10826

openalex publication_date 2024/04/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Cited by

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

Related

• Cycles on the Moduli Space of Abelian Varieties
• Generic Torelli with denominators for elliptic surfaces
• Noether-Lefschetz cycles on the moduli space of abelian varieties
• The Torelli map restricted to the hyperelliptic locus
• d-elliptic loci in genus 2 and 3