Néron models and the height jump divisor

Abstract

We define an algebraic analogue, in the case of jacobians of curves, of the height jump divisor introduced recently by R. Hain. We give explicit combinatorial formulae for the height jump for families of semistable curves using labelled reduction graphs. With these techniques we prove a conjecture of Hain on the effectivity of the height jump, and also give a new proof of a theorem of Tate, Silverman and Green on the variation of heights in families of abelian varieties.

arXiv comment39 pages. The middle sections of the paper have been re-ordered for clarity. In addition, the results from Section 11 of the previous version have been removed, as they depend on some other results which are as yet unpublished. The contents of the old Section 11 will appear in a later paper