Related papers: Invariance of the parametric Oka property

Let \pi :Z\to X be a holomorphic submersion of a complex manifold Z onto a complex manifold X and D\Subset X a 1-convex domain with strongly pseudoconvex boundary. We prove that under certain conditions there always exists a spray of \pi…

Let $G$ be a reductive complex Lie group and $K$ be a maximal compact subgroup of $G$. Let $X$ be a reduced Stein $G$-space and $Y$ be a $G$-elliptic manifold. We prove the following parametric equivariant Oka principle. The inclusion of…

In this paper we establish a basic version of the Oka principle for multivalued sections of ramified holomorphic maps h from a complex manifold Z onto a Stein manifold X. If the ramification locus of h projects into a closed complex…

Let $X$ be a connected Oka manifold, and let $S$ be a Stein manifold with $\mathrm{dim} S \geq \mathrm{dim} X$. We show that every continuous map $S\to X$ is homotopic to a surjective strongly dominating holomorphic map $S\to X$. We also…

We take the first step in the development of an equivariant version of modern, Gromov-style Oka theory. We define equivariant versions of the standard Oka property, ellipticity, and homotopy Runge property of complex manifolds, show that…

Let \(\overline \Omega\) be a compact strongly pseudoconvex domain with smooth boundary in a Stein manifold, and let \(h:Z\to \overline \Omega\) be a fibre bundle of H\"older-Zygmund class \(\Lambda^r\), \(r>0\), which is holomorphic over…

Let $X$ be an open Riemann surface. We prove an Oka property on the approximation and interpolation of continuous maps $X \to (\mathbb{C}^*)^2$ by proper holomorphic embeddings, provided that we permit a smooth deformation of the complex…

Let ${\mathcal A}\subset {\mathcal P}(X)$, $\emptyset, X\in {\mathcal A}$, ${\mathcal A}$ being closed under finite intersections. If $\psi={o},\omega,\gamma$, then $\Psi({\mathcal A})$ is the family of those $\psi$-covers ${\mathcal U}$…

This is a sequel to [Ca01]=math.AG/0110051. We define the bimeromorphic {\it category} of geometric orbifolds. These interpolate between (compact K\" ahler) manifolds and such manifolds with logarithmic structure. These geometric orbifolds…

Little is known about the behaviour of the Oka property of a complex manifold with respect to blowing up a submanifold. A manifold is of Class $\mathscr A$ if it is the complement of an algebraic subvariety of codimension at least $2$ in an…

A complex manifold $Y$ is said to have the interpolation property if a holomorphic map to $Y$ from a subvariety $S$ of a reduced Stein space $X$ has a holomorphic extension to $X$ if it has a continuous extension. Taking $S$ to be a…

Our main theorem states that the complement of a compact holomorphically convex set in a Stein manifold with the density property is an Oka manifold. This gives a positive answer to the well-known long-standing problem in Oka theory whether…

An elliptic curve $E$ defined over a $p$-adic field $K$ with a $p$-isogeny $\phi:E\rightarrow E^\prime$ comes equipped with an invariant $\alpha_{\phi/K}$ that measures the valuation of the leading term of the formal group homomorphism…

The scattering of electrons with polar optical phonons (POP) is an important mechanism that limits electronic transport and determines electron mobility in polar materials. This is typically a stronger mechanism compared to non-polar…

The conformal module of conjugacy classes of braids is an invariant that appeared earlier than the entropy of conjugacy classes of braids, and is inverse proportional to the entropy. Using the relation between the two invariants we give a…

Let $n>1$ be an integer. We prove that holomorphic maps from Stein manifolds $X$ of dimension $<n$ to the complement $\mathbb{C}^n\setminus L$ of a compact convex set $L\subset\mathbb{C}^n$ satisfy the basic Oka property with approximation…

We propose the scale-invariant intrinsic hyperpolarizability as a measure of the figure of merit for electrooptic molecules. By applying our analysis to the best second-order nonlinear-optical molecules that are made using the present…

Let Y be an infinite covering space of a projective manifold M in P^N of dimension n geq 2. Let C be the intersection with M of at most n-1 generic hypersurfaces of degree d in P^N. The preimage X of C in Y is a connected submanifold. Let…

We generalize the notion of the density property for complex manifolds to holomorphic fibrations, and introduce the notion of the fibred density property. We prove that the natural fibration of the spectral ball over the symmetrized…

The basic result of Oka theory, due to Gromov, states that every continuous map $f$ from a Stein manifold $S$ to an elliptic manifold $X$ can be deformed to a holomorphic map. It is natural to ask whether this can be done for all $f$ at…