Holomorphic families of $[\lambda]-$primitive themes

Abstract

This article is the continuation of [B. 13-b] where we show how the isomorphism class of a $[\lambda]-$primitive theme with a given Bernstein polynomial may be characterized by a (small) finite number of complex parameters. We construct here a corresponding locally versal holomorphic deformation of $ [\lambda]-$primitive themes for each given Bernstein polynomial. Then we prove the universality of the corresponding "canonical family" in many cases. We also give some examples where no local universal family exists.