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A compactification of ( * ) 4 with no non-constant meromorphic functions

Jun-Muk Hwang, Dror Varolin (2002)

Annales de l’institut Fourier

For each 2-dimensional complex torus T , we construct a compact complex manifold X ( T ) with a 2 -action, which compactifies ( * ) 4 such that the quotient of ( * ) 4 by the 2 -action is biholomorphic to T . For a general T , we show that X ( T ) has no non-constant meromorphic functions.

A description based on Schubert classes of cohomology of flag manifolds

Masaki Nakagawa (2008)

Fundamenta Mathematicae

We describe the integral cohomology rings of the flag manifolds of types Bₙ, Dₙ, G₂ and F₄ in terms of their Schubert classes. The main tool is the divided difference operators of Bernstein-Gelfand-Gelfand and Demazure. As an application, we compute the Chow rings of the corresponding complex algebraic groups, recovering thereby the results of R. Marlin.

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...

A KAM phenomenon for singular holomorphic vector fields

Laurent Stolovitch (2005)

Publications Mathématiques de l'IHÉS

Let X be a germ of holomorphic vector field at the origin of Cn and vanishing there. We assume that X is a good perturbation of a “nondegenerate” singular completely integrable system. The latter is associated to a family of linear diagonal vector fields which is assumed to have nontrivial polynomial first integrals (they are generated by the so called “resonant monomials”). We show that X admits many invariant analytic subsets in a neighborhood of the origin. These are biholomorphic to the intersection...

A weighted Plancherel formula II. The case of the ball

Genkai Zhang (1992)

Studia Mathematica

The group SU(1,d) acts naturally on the Hilbert space L ² ( B d μ α ) ( α > - 1 ) , where B is the unit ball of d and d μ α the weighted measure ( 1 - | z | ² ) α d m ( z ) . It is proved that the irreducible decomposition of the space has finitely many discrete parts and a continuous part. Each discrete part corresponds to a zero of the generalized Harish-Chandra c-function in the lower half plane. The discrete parts are studied via invariant Cauchy-Riemann operators. The representations on the discrete parts are equivalent to actions on some holomorphic...

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