Related papers: Steinness of bundles with fiber a Reinhardt bounde…

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…

A Steiner bundle over the projective 3-space is the kernel in a trivial bundle of a morphism defined by a matrix of linear forms. We produce various Steiner bundles E of rank n such that E(1) has n-1 sections, the dependency locus of which…

We consider a family E_m(D,M) of holomorphic bundles constructed as follows: to any given M in GL_n(Z), we associate a "multiplicative automorphism" f of (C*)^n. Now let D be a f-invariant Stein Reinhardt domain in (C*)^n. Then E_m(D,M) is…

The boundary of every relatively compact Stein domain in a complex manifold of dimension at least two is connected. No assumptions on the boundary regularity are necessary. The same proofs hold also for $q$-complete domains, and in the…

Let Z be a complex space and let S be a compact set in C^n x Z which is fibered over R^n (the real subspace of C^n). We give a necessary and sufficient condition for S to be a Stein compactum.

It is easy to imagine that a subvariety of a vector bundle, whose intersection with every fibre is a vector subspace of constant dimension, must necessarily be a sub-bundle. We give two examples to show that this is not true, and several…

Let $k$ be a non-archimedean complete valued field and $X$ be a $k$-analytic space in the sense of Berkovich. In this note, we prove the equivalence between three properties: 1) for every complete valued extension $k'$ of $k$, every…

In this paper we give a very simple proof of the existence and plenitude of Runge tubes in $\mathbb C^n$ $(n>1)$ and, more generally, in Stein manifolds with the density property. We show in particular that for any algebraic submanifold $A$…

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…

In section 1, we show that if $X$ is a Stein normal complex space of dimension n and $D\subset \subset X$ an open subset which is the union of an increasing sequence $D_{1}\subset D_{2}\subset ...\subset D_{n}\subset >...$ of domains of…

We give an example of a bounded Stein domain in $\mathbb{C}^n$, with smooth boundary, which is not Runge and whose intersection with every complex line is simply connected.

We study line bundles on smooth toric DM stacks $\mathbb{P}_{\mathbf{\Sigma}}$ of arbitrary dimension. A sufficient condition is given for when infinitely many line bundles on $\mathbb{P}_{\mathbf{\Sigma}}$ have trivial cohomology. In…

It is well-known that the associated analytic space of an affine variety defined over $\mathbb{C}$ is Stein but the converse is not true, that is, an algebraic Stein variety is not necessarily affine. In this paper, we give sufficient and…

Let E be a stable rank 2 vector bundle on a smooth quadric threefold Q in the projective 4-space P. We show that the hyperplanes H in P for which the restriction of E to the hyperplane section of Q by H is not stable form, in general, a…

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…

We prove that a Stein manifold of dimension $d$ admits a proper holomorphic embedding into any Stein manifold of dimension at least $2d+1$ satisfying the holomorphic density property. This generalizes classical theorems of Remmert, Bishop…

For an integer $n$, write $X_n(K)$ for the 4-manifold obtained by attaching a 2-handle to the 4-ball along the knot $K\subset S^3$ with framing $n$. It is known that if $n< \overline{\text{tb}}(K)$, then $X_n(K)$ admits the structure of a…

The main theorem of this article provides sufficient conditions for a degree $d$ finite cover $M'$ of a hyperbolic 3-manifold $M$ to be a surface-bundle. Let $F$ be an embedded, closed and orientable surface of genus $g$, close to a minimal…

Let $X$ be a compact connected Riemann surface and $(V, \phi)$ a holomorphic Lie algebroid on $X$ such that the holomorphic vector bundle $V$ is stable. We give a necessary and sufficient condition on holomorphic vector bundles $E$ on $X$…

We prove that certain vector bundles over surfaces are ample if they are so when restricted to divisors, certain numerical criteria hold, and they are semistable (with respect to $\det(E)$). This result is a higher-rank version of a theorem…