Compactifications of universal abelian threefolds with CM

We determine completions of semi-abelian degenerations of abelian threefolds with complex multiplication. This type of completion plays a crucial role in the determination of motivic decompositions of such degenerating families. To this end we generalize the notion of “relatively complete model” as introduced by Mumford, Faltings and Chai and explicitly compute it in the case at hand.