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

Daniel Barlet (1)

1 IECL - Institut Élie Cartan de Lorraine

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.

Mots clés: Theme; Vanishing period; Bernstein polynomial; (a; Brieskorn module; isomonodromic deformations; filtered Gauss-Manin system; b)-module

Domaines: Variables complexes [math.CV]; Géométrie algébrique [math.AG]; Mathématiques générales [math.GM]

Daniel Barlet. Holomorphic families of $[\lambda]-$primitive themes. 2015. ⟨hal-01184022⟩