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An obstruction to homogeneous manifolds being Kähler

Bruce Gilligan (2005)

Annales de l’institut Fourier

Let G be a connected complex Lie group, H a closed, complex subgroup of G and X : = G / H . Let R be the radical and S a maximal semisimple subgroup of G . Attempts to construct examples of noncompact manifolds X homogeneous under a nontrivial semidirect product G = S R with a not necessarily G -invariant Kähler metric motivated this paper. The S -orbit S / S H in X is Kähler. Thus S H is an algebraic subgroup of S [4]. The Kähler assumption on X ought to imply the S -action on the base Y of any homogeneous fibration X Y is algebraic...

An open mapping theorem for analytic multifunctions

Zbigniew Słodkowski (1997)

Studia Mathematica

The paper gives sufficient conditions for projections of certain pseudoconcave sets to be open. More specifically, it is shown that the range of an analytic set-valued function whose values are simply connected planar continua is open, provided there does not exist a point which belongs to boundaries of all the fibers. The main tool is a theorem on existence of analytic discs in certain polynomially convex hulls, obtained earlier by the author.

Analytic cohomology of complete intersections in a Banach space

Imre Patyi (2004)

Annales de l’institut Fourier

Let X be a Banach space with a countable unconditional basis (e.g., X = 2 ), Ω X an open set and f 1 , ... , f k complex-valued holomorphic functions on Ω , such that the Fréchet differentials d f 1 ( x ) , ... , d f k ( x ) are linearly independant over at each x Ω . We suppose that M = { x Ω : f 1 ( x ) = ... = f k ( x ) = 0 } is a complete intersection and we consider a holomorphic Banach vector bundle E M . If I (resp. 𝒪 E ) denote the ideal of germs of holomorphic functions on Ω that vanish on M (resp. the sheaf of germs of holomorphic sections of E ), then the sheaf cohomology groups H q ( Ω , I ) , H q ( M , 𝒪 E ) vanish...

Analytic convexity

Aldo Andreotti, Mauro Nacinovich (1980)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Currently displaying 441 – 460 of 608