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arXiv · 2302.05860

Abelian varieties are not quotients of low-dimension Jacobians

Jacob Tsimerman
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Abstract

We prove that for any two integers $g\geq 4$ and $g'\leq 2g-1$, there exist abelian varieties over $\overline{\mathbb{Q}}$ which are not quotients of a Jacobian of dimension $g'$. Our method in fact proves that most Abelian varieties satisfy this property, when counting by height relative to a fixed finite map to projective space.

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Jacob Tsimerman. 2023-02-12. Abelian varieties are not quotients of low-dimension Jacobians. https://arxiv.org/abs/2302.05860

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