On Strongly Pseudo-convex Kähler Manifolds.
On Surfaces of Class VII0 with Curves.
On the Chern Numbers of Surfaces of General Type.
On the determinant of the bundle of meromorphic quadratic differentials on the Deligne-Mumford compactification of the moduli space of Riemann surfaces.
On the Kählerian geometry of 1-convex threefolds.
On the Minimal Models of Complex Manifolds.
On the mixed Hodge structure associated to of a simply connected complex projective manifold
On the non-existence of Kähler structures on certain closed and oriented differentiable 6-manifolds.
On the number of non-equivalent differentiable structures on 4-Manifolds.
On the Picard number of a complex projective variety
On the volume of a pseudo-effective class and semi-positive properties of the Harder-Narasimhan filtration on a compact Hermitian manifold
This paper divides into two parts. Let (X,ω) be a compact Hermitian manifold. Firstly, if the Hermitian metric ω satisfies the assumption that for all k, we generalize the volume of the cohomology class in the Kähler setting to the Hermitian setting, and prove that the volume is always finite and the Grauert-Riemenschneider type criterion holds true, which is a partial answer to a conjecture posed by Boucksom. Secondly, we observe that if the anticanonical bundle is nef, then for any ε >...
Periods of Enriques Surfaces.
Permanence of local properties under hyperplane sections
Polarized Mixed Hodge Structures and the Local Monodromy of a Variation of Hodge Structure.
Projective varieties invariant by one-dimensional foliations.
Projectivity of Kähler manifolds – Kodaira’s problem
Every compact Kähler surface is deformation equivalent to a projective surface. In particular, topologically Kähler surfaces and projective surfaces cannot be distinguished. Kodaira had asked whether this continues to hold in higher dimensions. We explain the construction of a series of counter-examples due to C. Voisin, which yields compact Kähler manifolds of dimension at least four whose rational homotopy type is not realized by any projective manifold.
Proof of Nadel’s conjecture and direct image for relative -theory
A “relative” -theory group for holomorphic or algebraic vector bundles on a compact or quasiprojective complex manifold is constructed, and Chern-Simons type characteristic classes are defined on this group in the spirit of Nadel. In the projective case, their coincidence with the Abel-Jacobi image of the Chern classes of the bundles is proved. Some applications to families of holomorphic bundles are given and two Riemann-Roch type theorems are proved for these classes.
Remarques sur le revêtement universel des variétés kählériennes compactes
Réseaux de Kummer et surfaces K3.
Structure de Hodge mixte sur la cohomologie évanescente
Soit un morphisme propre d’un -schéma intègre dans un germe de courbe algébrique lisse sur . On construit une structure de Hodge mixte sur les cohomologies évanescentes en résolvant les complexes évanescents et par des complexes de Hodge mixtes cohomologiques. Ceci donne une majoration du niveau d’unipotence de l’action de la monodromie.