Fibrés vectoriels et cycles d'ordre fini sur une variété algébrique non compacte
Fields of CR meromorphic functions
Filtrations of meromorphic C* actions on complex manifolds.
Finiteness Results for Algebraic K3 Surfaces.
Formal cohomology, analytic cohomology and non-algebraic manifolds
Formale Geometrie und homogene Räume.
From non-Kählerian surfaces to Cremona group of P 2 (C)
For any minimal compact complex surface S with n = b2(S) > 0 containing global spherical shells (GSS) we study the effectiveness of the 2n parameters given by the n blown up points. There exists a family of surfaces S → B with GSS which contains as fibers S, some Inoue-Hirzebruch surface and non minimal surfaces, such that blown up points are generically effective parameters. These families are versal outside a non empty hypersurface T ⊂ B. We deduce that, for any configuration of rational curves,...
Generalized Intermediate Jacobians and the Theorem on Normal Functions.
Geometric algebraicity of moduli spaces of compact Kähler symplectic manifolds.
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,...
Geometrical properties of a family of compactifications.
Global smoothing of Calabi-Yau threefolds.
Globally invertible differentiable or holomorphic maps
Graph theoretic techniques in algebraic geometry II: construction of singular complex surfaces of the rational cohomology type of CP2.
Hermitian spin surfaces with small eigenvalues of the Dolbeault operator
We study the compact Hermitian spin surfaces with positive conformal scalar curvature on which the first eigenvalue of the Dolbeault operator of the spin structure is the smallest possible. We prove that such a surface is either a ruled surface or a Hopf surface. We give a complete classification of the ruled surfaces with this property. For the Hopf surfaces we obtain a partial classification and some examples
Hermitian-Einstein Connections and Stable Vector Bundles Over Compact Complex Surfaces.
Higher de Rham-Witt complexes of supersingular K3 surfaces
Hodge groups of K3 surfaces.
Hodge metrics and the curvature of higher direct images
Using the harmonic theory developed by Takegoshi for representation of relative cohomology and the framework of computation of curvature of direct image bundles by Berndtsson, we prove that the higher direct images by a smooth morphism of the relative canonical bundle twisted by a semi-positive vector bundle are locally free and semi-positively curved, when endowed with a suitable Hodge type metric.
Holomorphic actions, Kummer examples, and Zimmer program
We classify compact Kähler manifolds of dimension on which acts a lattice of an almost simple real Lie group of rank . This provides a new line in the so-called Zimmer program, and characterizes certain complex tori as compact Kähler manifolds with large automorphisms groups.