Related papers: Holomorphic flexibility properties of compact comp…

Using the Kodaira dimension and the fundamental group of X, we succeed in classifying algebraic surfaces which are dominable by C^2 except for certain cases in which X is an algebraic surface of Kodaira dimension zero and the case when X is…

Let X be a compact complex surface with a real foliation. If all leaves are compact complex curves, the foliation must be holomorphic.

It is a well-known and elementary fact that a holomorphic function on a compact complex manifold without boundary is necessarily constant. The purpose of the present article is to investigate whether, or to what extent, a similar property…

An n-dimensional complex manifold M is said to be (holomorphically) dominable by $\CC^n$ if there is a map $F:\CC^n \ra M$ which is holomorphic such that the Jacobian determinant $\det(DF)$ is not identically zero. Such a map F is called a…

Let $f$ be a holomorphic mapping between compact complex manifolds. We give a criterion for $f$ to have {\it unobstructed deformations}, i.e. for the local moduli space of $f$ to be smooth: this says, roughly speaking, that the group of…

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…

It is an elementary fact that the action by holomorphic automorphisms on C^n is infinitely transitive, i.e., m-transitive for any m in N. The same holds on any Stein manifold with the holomorphic density property X. We study a parametrized…

Assume that E and B are complex manifolds and that pi is a holomorphic Serre fibration from E onto E such that E admits a finite dominating family of holomorphic fiber-sprays over a small neighborhood of any point in B. We show that the…

In the last decades affine algebraic varieties and Stein manifolds with big (infinite-dimensional) automorphism groups have been intensively studied. Several notions expressing that the automorphisms group is big have been proposed. All of…

We study when there exists a dense holomorphic curve in a space of holomorphic maps from a Stein space. We first show that for any bounded convex domain $\Omega\Subset\mathbb{C}^n$ and any connected complex manifold $Y$, the space…

We give a proof of the following theorem of M. Gromov (Oka's principle for holomorphic sections of elliptic bundles, J. Amer. Math. Soc., 2 (1989), 851-897). Let Z be a holomorphic fiber bundle over a Stein manifold. If the fiber of Z…

We show that the universal cover of a compact complex surface $X$ is the bidisk $\HH \times \HH$, or $X$ is biholomorphic to $\PP^1 \times \PP^1$, if and only if $K_X^2 > 0$ and there exists an invertible sheaf $\eta$ such that $\eta^2\cong…

Let X be a Stein manifold and let Y be a complex manifold which admits a spray in the sense of Gromov (Oka's principle for holomorphic sections of elliptic bundles, J. Amer. Math. Soc. 2, pp. 851-897 (1989)). We prove that for every closed…

In this note, we show that the homotopy type of a complex manifold X satisfying the Oka property is captured by holomorphic maps from the affine spaces C^n, n\geq 0, into X. Among such X are all complex Lie groups and their homogeneous…

A complex manifold $X$ satisfies the Oka-Grauert property if the inclusion $\Cal O(S,X) \hookrightarrow \Cal C(S,X)$ is a weak equivalence for every Stein manifold $S$, where the spaces of holomorphic and continuous maps from $S$ to $X$ are…

We study the geometry of compact strong HKT and, more generally, compact BHE manifolds. We prove that any compact BHE manifold with full holonomy must be K\"ahler and we establish a similar result for strong HKT manifolds. Additionally, we…

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…

Suppose $k$ is an algebraically closed field of characteristic two, let $A_4$ be an alternating group on four letters, and let $H$ be the unique Sylow two-subgroup of $A_4$. Let $X$ be a smooth projective irreducible curve over $k$ with a…

We obtain results on approximation of holomorphic maps by algebraic maps, jet transversality theorems for holomorphic and algebraic maps, and the homotopy principle for holomorphic submersions of Stein manifolds to certain algebraic…

We study the Oka properties of complements of closed countable sets in $\mathbb{C}^{n}\ (n>1)$ which are not necessarily discrete. Our main result states that every tame closed countable set in $\mathbb{C}^{n}\ (n>1)$ with a discrete…