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Abelian varieties are not quotients of low-dimension Jacobians

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arxiv 2302.05860 v1 pith:6ULTKKGK submitted 2023-02-12 math.NT math.AG

Jacob Tsimerman This is my paper · ORCID
classification math.NTmath.AG
keywords abelianvarietiesquotientscountingdimensionexistfactfinite
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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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Cited by 2 Pith papers

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