A finiteness theorem for \ $S-$relative formal Brieskorn modules

Daniel Barlet (1)

1 IECL - Institut Élie Cartan de Lorraine

We give a general result of finiteness for holomorphic families of Brieskorn modules constructed from a holomorphic family of one parameter degeneration of compact complex manifolds acquiring (general) singularities.

Mots clés: filtered differential equation; Gauss-Manin connection; asymptotic expansion; Brieskorn module; (a; b)-module

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

Daniel Barlet. A finiteness theorem for \ $S-$relative formal Brieskorn modules. 2014. ⟨hal-00718606v2⟩