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SINGULARITIES OF THE BIEXTENSION METRIC FOR FAMILIES OF ABELIAN VARIETIES

Part of: Curves Arithmetic algebraic geometry Families, fibrations

Published online by Cambridge University Press:  23 July 2018

JOSÉ IGNACIO BURGOS GIL ,
DAVID HOLMES  and
ROBIN DE JONG
JOSÉ IGNACIO BURGOS GIL
Affiliation:
Instituto de Ciencias Matemáticas (CSIC-UAM-UCM-UCM3), Calle Nicolás Cabrera 15, Campus UAM, Cantoblanco, 28049 Madrid, Spain; [email protected]
DAVID HOLMES
Affiliation:
Mathematical Institute, Leiden University, PO Box 9512, 2300 RA Leiden, The Netherlands; [email protected], [email protected]
ROBIN DE JONG
Affiliation:
Mathematical Institute, Leiden University, PO Box 9512, 2300 RA Leiden, The Netherlands; [email protected], [email protected]

Abstract

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In this paper we study the singularities of the invariant metric of the Poincaré bundle over a family of abelian varieties and their duals over a base of arbitrary dimension. As an application of this study we prove the effectiveness of the height jump divisors for families of pointed abelian varieties. The effectiveness of the height jump divisor was conjectured by Hain in the more general case of variations of polarized Hodge structures of weight  $-1$ .

MSC classification

Primary: 14H10: Families, moduli (algebraic)
Secondary: 11G50: Heights 14D07: Variation of Hodge structures
Type
Research Article
Information
Forum of Mathematics, Sigma , Volume 6 , 2018 , e12
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Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s) 2018

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