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

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

2008-02-20

arxiv.org/abs/0802.2894v1

Mathematics

Algebraic Geometry

23 pages, in French, no figure

Scientific paper

In this article, we study some properties of deformation invariance of the Gamma-dimension (defined for X a compact k\"ahler 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 K\"ahler families of dimension 3.

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