A Contraction of S U (2) to the Heisenberg Group.
A geometry on the space of probabilities (II). Projective spaces and exponential families.
In this note we continue a theme taken up in part I, see [Gzyl and Recht: The geometry on the class of probabilities (I). The finite dimensional case. Rev. Mat. Iberoamericana 22 (2006), 545-558], namely to provide a geometric interpretation of exponential families as end points of geodesics of a non-metric connection in a function space. For that we characterize the space of probability densities as a projective space in the class of strictly positive functions, and these will be regarded as a...
Automorphismes analytiques des produits continus de domaines bornés
Biholomorphic Mappings and the Bergman kernel off the Diagonal.
-conjugacy of holomorphic flows near a singularity
Classification of singular germs of mappings and deformations of compact surfaces of class VII₀
We classify generic germs of contracting holomorphic mappings which factorize through blowing-ups, under the relation of conjugation by invertible germs of mappings. As for Hopf surfaces, this is the key to the study of compact complex surfaces with and which contain a global spherical shell. We study automorphisms and deformations and we show that these generic surfaces are endowed with a holomorphic foliation which is unique and stable under any deformation.
Compact quotients of large domains in complex projective space
We study compact complex manifolds covered by a domain in -dimensional projective space whose complement is non-empty with -dimensional Hausdorff measure zero. Such manifolds only exist for . They do not belong to the class , so they are neither Kähler nor Moishezon, their Kodaira dimension is , their fundamental groups are generalized Kleinian groups, and they are rationally chain connected. We also consider the two main classes of known 3-dimensional examples: Blanchard manifolds, for which...
Complex-symmetric spaces
A compact complex space is called complex-symmetric with respect to a subgroup of the group , if each point of is isolated fixed point of an involutive automorphism of . It follows that is almost -homogeneous. After some examples we classify normal complex-symmetric varieties with reductive. It turns out that is a product of a Hermitian symmetric space and a compact torus embedding satisfying some additional conditions. In the smooth case these torus embeddings are classified using...
Deformations of Holomorphic Group Actions.
Derivations of the Lie algebras of analytic vector fields
Domaines de , pseudoconvexes et de type fini ayant un groupe non compact d’automorphismes
On démontre que les domaines bornés, pseudo-convexes, à frontière lisse, de type fini dans , ayant un groupe d’automorphismes non compact sont biholomorphes à des domaines de la forme , où est un polynôme sousharmonique dont le degré est majoré par le type de la frontière du domaine.
Extension Theorems for Reductive Group Actions on Compact Kaehler Manifolds.
Fixpunktmengen kompakter Gruppen in Teilgebieten Steinscher Mannigfaltigkeiten.
Holomorphe Blätterungen komplexer Räume
Homogeneous Cauchy-Riemann structures
Kompakte Transformationsgruppen Steinscher Räume.
Moduli of Open Holomorphic Maps of Compact Complex Manifolds.
New representation of the non-symmetric homogeneous bounded domains in and .
On Automorphisms of Complements of Analytic Subsets in Cn.
On Compact Complex Manifolds with Finite Automorphism Group
It is known that compact complex manifolds of general type and Kobayashi hyperbolic manifolds have finite automorphism groups. We give criteria for finiteness of the automorphism group of a compact complex manifold which allow us to produce large classes of compact complex manifolds with finite automorphism group but which are neither of general type nor Kobayashi hyperbolic.