Geodesic
Smooth hypersurfaces in abelian varieties over arithmetic rings
Forum of Mathematics, Sigma, Tome 10 (2022)

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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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     author = {Ariyan Javanpeykar and Siddharth Mathur},
     title = {Smooth hypersurfaces in abelian varieties over arithmetic rings},
     journal = {Forum of Mathematics, Sigma},
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     year = {2022},
     doi = {10.1017/fms.2022.87},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/fms.2022.87/}
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Ariyan Javanpeykar; Siddharth Mathur. Smooth hypersurfaces in abelian varieties over arithmetic rings. Forum of Mathematics, Sigma, Tome 10 (2022). doi: 10.1017/fms.2022.87

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