Smooth hypersurfaces in abelian varieties over arithmetic rings

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2022

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CC-BY-4.0
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Item type: Item , ZeitschriftenaufsatzAccess status: Open Access ,

Abstract

Let A be an abelian scheme of dimension at least four over a 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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http://doi.org/10.25358/openscience-8815

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https://openscience.ub.uni-mainz.de/handle/20.500.12030/8831

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Forum of Mathematics, Sigma, 10, Cambridge University Press, Cambridge, 2022, https://doi.org/10.1017/fms.2022.87

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