Singularities of the biextension metric for families of abelian   varieties
  In this paper we study the singularities of the invariant metric of the Poincar\'e 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 $-1$. 
Jose Ignacio Burgos Gil, David Holmes and Robin de Jong
math.AG