Strongly quasi-proper maps and the f-flattning theorem

Daniel Barlet (1)

1 IECL - Institut Élie Cartan de Lorraine

We complete and precise the results of [B.13] and we prove a strong version of the semi-proper direct image theorem with values in the space C f n (M) of finite type closed n−cycles in a complex space M. We describe the strongly quasi-proper maps as the class of holomorphic surjective maps which admit a meromorphic family of fibers and we prove stability properties of this class. In the Appendix we give a direct and short proof of D. Mathieu's flattning theorem (see [M.00]) for a strongly quasi-proper map which is easier and more accessible.

Mots clés: Finite Type Cycles; Semi-Proper Direct Image; Strongly Quasi-Proper map; Stein Factorization; Geometrically f-Flat map

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

Daniel Barlet. Strongly quasi-proper maps and the f-flattning theorem. 2015. ⟨hal-01139915⟩