Completion of two-parameter period maps by nilpotent orbits

Abstract

We show that every two-parameter period map admits a Kato--Nakayama--Usui completion to a morphism of log manifolds, and the map onto the image is a morphism of compact algebraic spaces. This result also applies to the case of mixed period maps and we use it to give a construction of generalized Nèron models.

v2: Major revision. The proof of the main finiteness theorem (theorem 2.27) is now fixed