Invariance de la Gamma-dimension pour certaines familles kählériennes de dimension 3

Benoît Claudon (1)

1 IECN - Institut Élie Cartan de Nancy

In this article, we study some properties of deformation invariance of the Gamma-dimension (defined for X a compact kähler manifold). This birational invariant is defined as the codimension of the maximal compact subvarieties in the universal cover of X. In the surface case, the deformation invariance is a straightforward consequence of a theorem of Y.-T. Siu. Using some results from F. Campana et Q. Zhang, we settle this invariance for certain type of Kähler families of dimension 3.

Mots clés: Gamma-reduction; smooth family; deformation invariance; fundamental group

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

Benoît Claudon. Invariance de la Gamma-dimension pour certaines familles kählériennes de dimension 3. Mathematische Zeitschrift, 2010, 266 (2), pp.265-284. ⟨hal-00257966⟩