Related papers: Fibrations and Stein Neighborhoods

In this paper, we show that a compact real surface embedded in a complex surface has a regular Stein neighborhood basis, provided that there are only finitely many complex points on the surface, and that they are all flat and hyperbolic. An…

In this paper we provide sufficient conditions for the graphs of holomorphic mappings on compact sets in complex manifolds to have Stein neighborhoods. We show that under these conditions the mappings have properties analogous to properties…

In this paper we construct open Stein neighbourhoods of compact sets of the form $A\cup K$ in a complex space, where $K$ is a compact holomorphically convex set, $A$ is a compact complex curve with boundary $bA$ of class $\mathscr C^2$…

We show: If a bounded domain in a Stein space covers a compact complex space, it must be smooth. This give a negative answer to a question of Koll\'ar. Furthermore, we deduce some related results.

Let E denote a bundle with fiber D and with basis B. Both D and B are assumed to be Stein. For D a Reinhardt bounded domain of dimension d=2 or 3, we give a necessary and sufficient condition on D for the existence of a non-Stein such E…

We give a characterization of the complex Euclidean space C^n, proving a global Newlander-Nirenberg's theorem on the representability of complex structures close to the standard complex structure on C^n.

Let $G$ be a topological group and let $K,L\subseteq G$ be closed subgroups, with $K\subseteq L$. We prove that if $L$ is a locally compact pro-Lie group, then the map $q:G/K\to G/L$ is a fibration. As an application of this, we obtain two…

Let X be an irreducible reduced complex space on which a connected compact Lie group K acts by holomorphic automorphisms. Let G be the complexification of K and g the Lie algebra of G. Following the theory of algebraic transformation…

Let D be a smooth bounded pseudoconvex domain in C^n. We give several characterizations for the closure of D to have a strong Stein neighborhood basis in the sense that D has a defining function r such that {z\in C^n:r(z)<a} is pseudoconvex…

We give a geometric condition on a compact subset of a complex manifold which is necessary and sufficient for the existence of a smooth strictly plurisubharmonic function defined in a neighbourhood of this set.

A necessary and sufficient compactness criterion in Schauder Spaces is proved.

Given a projective or compact K\"ahler manifold X and a (smooth) hypersurface Y, we study conditions under which $X \setminus Y$ could be Stein. We apply this in particular to the case when X is the projectivization of the so-called…

In this paper we construct a Stein neighborhood basis for any compact subvariety $A$ with strongly pseudoconvex boundary $bA$ and Stein interior $A\backslash bA$ in a complex space $X$. This is an extension of a well known theorem of Siu.…

This paper is concerned with "nice" compactifications of manifolds. Siebenmann's iconic dissertation characterized open manifolds M^m (m>5) compactifiable by addition of a manifold boundary. His theorem extends easily to cases where M^m is…

It is proved that an unbranched Riemann domain $\Pi : X\rightarrow Y$ over an arbitrary Stein complex space of dimension $n\geq 2$ is Stein if and only if $X$ is cohomologically $2$-complete with respect to the structure sheaf…

Let $f \colon \mathbb{R}^n \rightarrow \mathbb{R}$ be a polynomial and $\mathcal{Z}(f)$ its zero set. In this paper, in terms of the so-called Newton polyhedron of $f,$ we present a necessary criterion and a sufficient condition for the…

We discuss various problems regarding the structure of the foliation of some foliated submanifolds S of C^n, in particular Levi flat ones. As a general scheme, we suppose that S is bounded along a coordinate (or a subset of coordinates),…

We prove that if a compact line is fragmentable, then it is a Radon-Nikod\'ym compact space.

We combine Freedman's topology with Eliashberg's holomorphic theory to construct Stein neighborhood systems in complex surfaces, and use these to study various notions of convexity and concavity. Every tame, topologically embedded 2-complex…

Let G be a connected semisimple linear algebraic group over an algebraically closed field k of positive characteristic and let X denote an equivariant embedding of G. We define a distinguished Steinberg fiber N in G, called the zero-fiber,…