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

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.

preprint2008arXivOpen access
Benoît Claudon
math.CVmath.AG
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Benoît Claudon

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