We show that in every dimension greater than or equal to 4, there exist compact Kaehler manifolds which do not have the homotopy type of projective complex manifolds. Thus they a fortiori are not deformation equivalent to a projective manifold, which solves negatively Kodaira's problem. We give both non simply connected (of dimension at least 4) and simply connected (of dimension at least 6) such examples
A complex ball quotient can be smoothly compactified to be a projective algebraic manifold. It is in...
International audienceWe introduce the concept of a branched holomorphic Cartan geometry. It general...
International audienceWe introduce the concept of a branched holomorphic Cartan geometry. It general...
In small dimensions, it is known that Kähler compact manifolds are deformation equivalent to smooth...
The celebrated Kodaira theorem [6] says that a compact complex manifold is projective if and only if...
The first example of a compact manifold admitting both complex and symplectic structures but not adm...
Abstract. We provide infinitely many examples of pairs of diffeomorphic, non simply connected Kähle...
This talk is concerned with questions arising from the problem of classification of compact complex ...
Let M_1 and M_2 be two Kaehler manifolds. We call M_1 and M_2 relatives if they share a non-trivia...
Abstract. In this paper we describe the construction of a new class of non-Kähler compact complex m...
In this paper, we study properties of some birational invariants of a complex variety and a fibred s...
Simply connected compact Kahler manifolds of dimension up to three with elliptic homotopy type are c...
The aim of this paper is to continue the study of Kodaira dimension for almost complex manifolds, fo...
In the first part of my thesis we provide infinitely many examples of pairs of diffeomorphic, non si...
AbstractThe principle “ambient cohomology of a Kaehler manifold annihilates obstructions” has been k...
A complex ball quotient can be smoothly compactified to be a projective algebraic manifold. It is in...
International audienceWe introduce the concept of a branched holomorphic Cartan geometry. It general...
International audienceWe introduce the concept of a branched holomorphic Cartan geometry. It general...
In small dimensions, it is known that Kähler compact manifolds are deformation equivalent to smooth...
The celebrated Kodaira theorem [6] says that a compact complex manifold is projective if and only if...
The first example of a compact manifold admitting both complex and symplectic structures but not adm...
Abstract. We provide infinitely many examples of pairs of diffeomorphic, non simply connected Kähle...
This talk is concerned with questions arising from the problem of classification of compact complex ...
Let M_1 and M_2 be two Kaehler manifolds. We call M_1 and M_2 relatives if they share a non-trivia...
Abstract. In this paper we describe the construction of a new class of non-Kähler compact complex m...
In this paper, we study properties of some birational invariants of a complex variety and a fibred s...
Simply connected compact Kahler manifolds of dimension up to three with elliptic homotopy type are c...
The aim of this paper is to continue the study of Kodaira dimension for almost complex manifolds, fo...
In the first part of my thesis we provide infinitely many examples of pairs of diffeomorphic, non si...
AbstractThe principle “ambient cohomology of a Kaehler manifold annihilates obstructions” has been k...
A complex ball quotient can be smoothly compactified to be a projective algebraic manifold. It is in...
International audienceWe introduce the concept of a branched holomorphic Cartan geometry. It general...
International audienceWe introduce the concept of a branched holomorphic Cartan geometry. It general...