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arXiv · 2205.09720

Smooth hypersurfaces in abelian varieties over arithmetic rings

Ariyan Javanpeykar·Siddharth Mathur
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Abstract

Let $A$ be an abelian scheme of dimension at least four over a $\mathbb{Z}$-finitely generated integral domain $R$ of characteristic zero, and let $L$ be an ample line bundle on $A$. We prove that the set of smooth hypersurfaces $D$ in $A$ representing $L$ is finite by showing that the moduli stack of such hypersurfaces has only finitely many $R$-points. We accomplish this by using level structures to interpolate finiteness results between this moduli stack and the stack of canonically polarized varieties.

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Ariyan Javanpeykar, Siddharth Mathur. 2022-05-19. Smooth hypersurfaces in abelian varieties over arithmetic rings. https://arxiv.org/abs/2205.09720

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