et -cohomologies d’une variété compacte privée d’un point. Application à l’intégration sur les cycles
Deformations of Kähler manifolds with nonvanishing holomorphic vector fields
We study compact Kähler manifolds admitting nonvanishing holomorphic vector fields, extending the classical birational classification of projective varieties with tangent vector fields to a classification modulo deformation in the Kähler case, and biholomorphic in the projective case. We introduce and analyze a new class of , and show that they form a smooth subspace in the Kuranishi space of deformations of the complex structure of . We extend Calabi’s theorem on the structure of compact Kähler...
Degeneracy of holomorphic maps via orbifolds
We use orbifold structures to deduce degeneracy statements for holomorphic maps into logarithmic surfaces. We improve former results in the smooth case and generalize them to singular pairs. In particular, we give applications on nodal surfaces and complements of singular plane curves.
Deux exemples sur la dimension moyenne d’un espace de courbes de Brody
On étudie la dimension moyenne de l’espace de courbes -Brody à valeurs dans deux surfaces complexes : d’abord pour des surfaces de Hopf, et ensuite pour privé d’une droite. On montre dans le premier cas que la dimension moyenne est nulle via une borne sur la croissance des fonctions holomorphes faisant apparaître le lemme de la dérivée logarithmique. Pour montrer la positivité dans le deuxième exemple, on relève de la droite à son complémentaire un espace de courbes de Brody de dimension moyenne...
Diastatic entropy and rigidity of complex hyperbolic manifolds
Let f : Y → X be a continuous map between a compact real analytic Kähler manifold (Y, g) and a compact complex hyperbolic manifold (X, g0). In this paper we give a lower bound of the diastatic entropy of (Y, g) in terms of the diastatic entropy of (X, g0) and the degree of f . When the lower bound is attained we get geometric rigidity theorems for the diastatic entropy analogous to the ones obtained by G. Besson, G. Courtois and S. Gallot [2] for the volume entropy. As a corollary,when X = Y,we...
Dirichlet domains for the Mostow lattices.
Domains with Pseudoconvex Neighborhood Systems.