  We are interested in classifying groups of local biholomorphisms (or even
formal diffeomorphisms) that can be endowed with a canonical structure of
algebraic group up to add extra formal diffeomorphisms. We show that this is
the case for virtually polycyclic subgroups and in particular finitely
generated virtually nilpotent groups of local biholomorphisms. We provide
several methods to identify this property and build examples.
  As a consequence we generalize results of Arnold, Seigal-Yakovenko and
Binyamini on uniform estimates of local intersection multiplicities to bigger
classes of groups, including for example virtually polycyclic groups.

Dynamical Systems;Complex Variables