Geodesic
SINGULARITIES OF THE BIEXTENSION METRIC FOR FAMILIES OF ABELIAN VARIETIES
Forum of Mathematics, Sigma, Tome 6 (2018)

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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 $-1$ . 
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     author = {JOS\'E IGNACIO BURGOS GIL and DAVID HOLMES and ROBIN DE JONG},
     title = {SINGULARITIES {OF} {THE} {BIEXTENSION} {METRIC} {FOR} {FAMILIES} {OF} {ABELIAN} {VARIETIES}},
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JOSÉ IGNACIO BURGOS GIL; DAVID HOLMES; ROBIN DE JONG. SINGULARITIES OF THE BIEXTENSION METRIC FOR FAMILIES OF ABELIAN VARIETIES. Forum of Mathematics, Sigma, Tome 6 (2018). doi: 10.1017/fms.2018.13

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