Page 1 Next

Displaying 1 – 20 of 32

Showing per page

A geometry on the space of probabilities (II). Projective spaces and exponential families.

Henryk Gzyl, Lázaro Recht (2006)

Revista Matemática Iberoamericana

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...

Classification of singular germs of mappings and deformations of compact surfaces of class VII₀

Georges Dloussky, Franz Kohler (1998)

Annales Polonici Mathematici

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 b 1 = 1 and b > 0 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

Finnur Lárusson (1998)

Annales de l'institut Fourier

We study compact complex manifolds covered by a domain in n -dimensional projective space whose complement E is non-empty with ( 2 n - 2 ) -dimensional Hausdorff measure zero. Such manifolds only exist for n 3 . They do not belong to the class 𝒞 , 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

Ralf Lehmann (1989)

Annales de l'institut Fourier

A compact complex space X is called complex-symmetric with respect to a subgroup G of the group Aut 0 ( X ) , if each point of X is isolated fixed point of an involutive automorphism of G . It follows that G is almost G 0 -homogeneous. After some examples we classify normal complex-symmetric varieties with G 0 reductive. It turns out that X 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...

On Compact Complex Manifolds with Finite Automorphism Group

Konrad Czaja (2005)

Bulletin of the Polish Academy of Sciences. Mathematics

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.

Currently displaying 1 – 20 of 32

Page 1 Next