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Benoît Claudon

Publications and source records attributed to Benoît Claudon.

26 records · Page 2Linked to original sources
arXiv2010

Threefolds with quasi-projective universal cover

We study compact Kähler threefolds X with infinite fundamental group whose universal cover can be compactified. Combining techniques from $L^2$ -theory, Campana's geometric orbifolds and the minimal model program we show that this condition imposes strong restrictions on the geometry of X. In particular we prove that if a projective threefold with infinite fundamental group has a quasi-projective universal cover, the latter is then isomorphic to the product of an affine space with a simply connected manifold.

math.AG↗
arXiv2010

Non algebraicity of universal cover of Kähler surfaces

In this short note, we study compact Kähler surfaces whose universal cover can be realized as a quasi-projective (or quasi-Kähler) surface. In particular, we show that such a surface is a quotient of a torus if the universal cover is affine.

math.AG↗
arXiv2009

Remarques sur la cohomologie des groupes kählériens nilpotents

In this note, we show that the cohomology groups of (virtually) nilpotent Kähler groups are naturally endowed with a mixed Hodge structure. These structures make the Hopf morphisms into mixed Hodge structures morphisms. We illustrate this fact with the study of known examples of non-abelian nilpotent Kähler groups.

math.AG↗
arXiv2008

Convexité holomorphe du revêtement de Malcev d'après S. Leroy

In these notes, we present the strategy employed by S. Leroy to attack the nilpotent case of the Shafarevich conjecture. The projective case was treated in a paper of L. Katzarkov but Leroy's proof is largely independant and works in the Kähler setting as well. It is entirely based on the higher Albanese manifolds constructed by R. Hain.

math.AG↗
arXiv2008

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.

math.AG↗
arXiv2008

Gamma-reduction for smooth orbifolds

The aim of this short note is to show how to construct a rationnal Remmert reduction for the universal cover of a smooth Kähler orbifold. Doins this, we are led to introduce some singular Kähler metrics adapted to the orbifold structure.

math.AG↗
arXiv2006

Invariance for multiples of the twisted canonical bundle

In this paper, we show an extension type theorem for twisted pluricanonical sections on a family of smooth projective manifolds (the twisting line bundle being pseudo-effective and having a prescribed multiplier ideal on the central fiber).

math.AG↗