A Geometric Study of the Monodromy of Complex Analytic Surfaces.
Ambient Deformations for Exceptional Sets in Two-Manifolds.
Analytic disks with boundaries in a maximal real submanifold of
Let be a two dimensional totally real submanifold of class in . A continuous map of the closed unit disk into that is holomorphic on the open disk and maps its boundary into is called an analytic disk with boundary in . Given an initial immersed analytic disk with boundary in , we describe the existence and behavior of analytic disks near with boundaries in small perturbations of in terms of the homology class of the closed curve in . We also prove a regularity theorem...
Compactifications kähleriennes de voisinages ouverts de cycles géométriquement positifs
Darstellbarkeitskriterien für analytische Funktoren
Deformation of Submanifolds of Strongly Negatively Curved Manifolds.
Deformation of Varieties Defined by Sections in Homogeneous Vector Bundles.
Deformationen von Keimen eigentlicher, holomorpher Abbildungen.
Déformations à nombre de Milnor constant : quelques résultats sur les polynômes de Bernstein
Deformations of coherent foliations on a compact normal space
An universal analytic structure is construted on the set of (singular) holomorphic foliations on a normal compact space. Such a foliation is by definition a coherent subsheaf of the holomorphic tangent sheaf stable by the Lie-bracket
Earthquakes are analytic.
Eine Künneth-Formel für die Tangentialkohomologie kompakter komplexer Räume.
Erratum to the paper : “Déformations à nombre de Milnor constant: quelques résultats sur les polynômes de Bernstein”
Etude topologique des formes logarithmiques fermées.
Families of varieties with prescribed singularities
Infinitesimal deformations of complex surfaces with boundary.
Invariance for multiples of the twisted canonical bundle
Let a smooth projective family and a pseudo-effective line bundle on (i.e. with a non-negative curvature current ). In its works on invariance of plurigenera, Y.-T. Siu was interested in extending sections of (defined over the central fiber of the family ) to sections of . In this article we consider the following problem: to extend sections of . More precisely, we show the following result: assuming the triviality of the multiplier ideal sheaf , any section of extends to ; in other...
Lagrangian fibrations on hyperkähler manifolds – On a question of Beauville
Let be a compact hyperkähler manifold containing a complex torus as a Lagrangian subvariety. Beauville posed the question whether admits a Lagrangian fibration with fibre . We show that this is indeed the case if is not projective. If is projective we find an almost holomorphic Lagrangian fibration with fibre under additional assumptions on the pair , which can be formulated in topological or deformation-theoretic terms. Moreover, we show that for any such almost holomorphic Lagrangian...
Moduli of Polarized Kahler Manifolds.
On the Smoothing and Deformation of Perfect Varieties.