A Theorem of Versality for Unfoldings of Complex Analytic Foliation Singularities.
Characterization of the complex projective space by holomorphic vector fields.
Cohomology of Compact Hyperkähler Manifolds and its Applications.
Complex analytic construction of the Kuranishi Family on a normal strongly pseudo convex manifold with real dimension 5.
Contact geometry and CR-structures on spheres
A normal form for small CR-deformations of the standard CR-structure on the (2n+1)-sphere is presented. The space of normal forms is parameterized by a single function on the sphere. For n>1, the normal form is used to obtain explicit embeddings into . For n=1, the cohomological obstruction to embeddability is identified.
Cyclic Coverings: Deformation and Torelli Theorem.
Decomposition of CR-manifolds and splitting of CR-maps
We show the uniqueness of local and global decompositions of abstract CR-manifolds into direct products of irreducible factors, and a splitting property for their CR-diffeomorphisms into direct products with respect to these decompositions. The assumptions on the manifolds are finite non-degeneracy and finite-type on a dense subset. In the real-analytic case, these are the standard assumptions that appear in many other questions. In the smooth case, the assumptions cannot be weakened by replacing...
Deformations of a complex mainfold near a strongly pseudo-convex real hypersurface and a realization of Kuranishi family of strongly pseudo-convex CR structures.
Deformations of Kähler manifolds with nonvanishing holomorphic vector fields
We study compact Kähler manifolds admitting nonvanishing holomorphic vector fields, extending the classical birational classification of projective varieties with tangent vector fields to a classification modulo deformation in the Kähler case, and biholomorphic in the projective case. We introduce and analyze a new class of , and show that they form a smooth subspace in the Kuranishi space of deformations of the complex structure of . We extend Calabi’s theorem on the structure of compact Kähler...
Deformations of Strictly Pseudoconvex Domains.
Deformations of transversely holomorphic flows on spheres and deformations of hopf manifolds
Earthquakes are analytic.
Embeddability of real analytic Cauchy-Riemann manifolds
Equivariant connected sums of compact self-dual manifolds.
Existence and Degeneration of Kähler-Einstein Metrics on Minimal Algebraic Varieties of General Type.
Factorization of rank two theta functions. II. Proof of the Verlinde formula.
Flag Structures on Seifert Manifolds.
Foliated structure of the Kuranishi space and isomorphisms of deformation families of compact complex manifolds
Consider the following uniformization problem. Take two holomorphic (parametrized by some analytic set defined on a neighborhood of in , for some ) or differentiable (parametrized by an open neighborhood of in , for some ) deformation families of compact complex manifolds. Assume they are pointwise isomorphic, that is for each point of the parameter space, the fiber over of the first family is biholomorphic to the fiber over of the second family. Then, under which conditions are the...
Homogeneous -hypersurface-structures on spheres
Local degeneration of the moduli space of vector bundles and factorization of rank two theta functions. I.