Vol. 8, No. 5, 2014

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ISSN: 1944-7833 (e-only)
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Polarization estimates for abelian varieties

David Masser and Gisbert Wüstholz

Vol. 8 (2014), No. 5, 1045–1070

In an earlier paper we showed that an abelian variety over a number field of fixed degree has a polarization whose degree is bounded by a power of its logarithmic Faltings height, provided there are only trivial endomorphisms. Here we greatly relax the endomorphism hypothesis, and we even eliminate it completely when the dimension is at most seven. Our methods ultimately go back to transcendence theory, with the asymmetric geometry of numbers as a new ingredient, together with what we call the Severi–Néron group, a variant of the Néron–Severi group.

abelian varieties, estimating polarizations
Mathematical Subject Classification 2010
Primary: 11G10
Secondary: 11J95
Received: 22 April 2013
Revised: 13 December 2013
Accepted: 15 February 2014
Published: 16 September 2014
David Masser
Mathematisches Institut
Universität Basel
CH-4051 Basel
Gisbert Wüstholz
Departement für Mathematik
CH-8092 Zürich