Authors:	Javanpeykar, Ariyan Mathur, Siddharth
Title:	Smooth hypersurfaces in abelian varieties over arithmetic rings
Online publication date:	27-Apr-2023
Year of first publication:	2022
Language:	english
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.
DDC:	510 Mathematik 510 Mathematics
Institution:	Johannes Gutenberg-Universität Mainz
Department:	FB 08 Physik, Mathematik u. Informatik
Place:	Mainz
ROR:	https://ror.org/023b0x485
DOI:	http://doi.org/10.25358/openscience-8815
Version:	Published version
Publication type:	Zeitschriftenaufsatz
Document type specification:	Scientific article
License:	CC BY
Information on rights of use:	https://creativecommons.org/licenses/by/4.0/
Journal:	Forum of Mathematics, Sigma 10
Pages or article number:	1 14
Publisher:	Cambridge University Press
Publisher place:	Cambridge
Issue date:	2022
ISSN:	2050-5094
Publisher DOI:	10.1017/fms.2022.87
Appears in collections:	DFG-491381577-H