-Geometrie omogenee e uniformizzazione
Gauge theoretical methods in the classification of non-Kählerian surfaces
The classification of class VII surfaces is a very difficult classical problem in complex geometry. It is considered by experts to be the most important gap in the Enriques-Kodaira classification table for complex surfaces. The standard conjecture concerning this problem states that any minimal class VII surface with b₂ > 0 has b₂ curves. By the results of [Ka1]-[Ka3], [Na1]-[Na3], [DOT], [OT] this conjecture (if true) would solve the classification problem completely. We explain a new approach...
Geometric stability of the cotangent bundle and the universal cover of a projective manifold
We first prove a strengthening of Miyaoka’s generic semi-positivity theorem: the quotients of the tensor powers of the cotangent bundle of a non-uniruled complex projective manifold have a pseudo-effective (instead of generically nef) determinant. A first consequence is that is of general type if its cotangent bundle contains a subsheaf with ‘big’ determinant. Among other applications, we deduce that if the universal cover of is not covered by compact positive-dimensional analytic subsets,...
Geometry of Kähler metrics and foliations by holomorphic discs
Geometry of the Complex Homogeneous Monge-Ampère Equation.
Geometry of the Kepler system in coherent states approach
Geometry of universal embedding spaces for almost complex manifolds
We investigate the geometry of universal embedding spaces for compact almost-complex manifolds of a given dimension, and related constructions that allow for an extrinsic study of the integrability of almost-complex structures. These embedding spaces were introduced by J-P. Demailly and H. Gaussier, and are complex algebraic analogues of twistor spaces. Their goal was to study a conjecture made by F. Bogomolov asserting the “transverse embeddability” of arbitrary compact complex manifolds into foliated...
Global boundary regularity for the -equation on -pseudo-convex domains
For a bounded domain of , we introduce a notion of «-pseudoconvexity» of new type and prove that for a given -closed -form that is smooth up to the boundary on , and for , there exists a -form smooth up to the boundary on which is a solution of the equation
Gluing complex discs to Lagrangian manifolds by Gromov’s method
The paper discusses some aspects of Gromov’s theory of gluing complex discs to Lagrangian manifolds.
Groupes triangulaires lagrangiens en géométrie hyperbolique complexe
Nous présentons quelques résultats au sujet des groupes engendrés par trois involutions antiholomorphes dans le cadre du plan hyperbolique complexe .