Related papers: A characterization of surfaces whose universal cov…

It is known that the universal cover of compact Riemann surface is either the projective line, the complex plane or the unit disk. In this article we construct a very explicit family of complex surfaces that gives rise to uncountably many…

We investigate a necessary condition for a compact complex manifold X of dimension n in order that its universal cover be the Cartesian product $C^n$ of a curve $C = \PP^1 or \HH$: the existence of a semispecial tensor $\omega$. A…

We give a short proof that, for nice $X$, the based fundamental groupoid of $X$ with topology induced by the compact open topology on the space of paths, is indeed the universal covering space of $X$.

In this paper, we study necessary and sufficient conditions for the existence of categorical universal coverings using open covers of a given space $X$. As some applications, first we present a generalized version of the Shelah Theorem…

We construct two complex-conjugated rigid surfaces with $p_g=q=2$ and $K^2=8$ whose universal cover is not biholomorphic to the bidisk. We show that these are the unique surfaces with these invariants and Albanese map of degree $2$, apart…

We introduce the notion of a stratified Oka manifold and prove that such a manifold $X$ is strongly dominable in the sense that for every $x\in X$, there is a holomorphic map $f:\C^n\to X$, $n=\dim X$, such that $f(0)=x$ and $f$ is a local…

We shall show that a smooth, quasi-projective variety $X$ has a holomorphically convex universal covering $\wt X$ when (i) $\pi_1(X)$ is residually nilpotent and (ii) there is an admissable variation of \mhs\ over $X$ whose monodromy…

We study the homeomorphism types of certain covers of (always orientable) surfaces, usually of infinite-type. We show that every surface with non-abelian fundamental group is covered by every noncompact surface, we identify the universal…

We construct a new surface of general type with p_g=0 and K^2=8 and prove that its universal cover can not be the bidisc.

The classical Shafarevich conjecture predicts that the universal cover of a complex smooth projective variety $X$ is holomorphically convex. In this paper, we propose a refinement of this conjecture for varieties defined over the reals. In…

A topological space (not necessarily simply connected) is said to have finite homotopy rank-sum if the sum of the ranks of all higher homotopy groups (from the second homotopy group onward) is finite. In this article, we characterize the…

We develop a generalized covering space theory for a class of uniform spaces called coverable spaces. Coverable spaces include all geodesic metric spaces, connected and locally pathwise connected compact topological spaces, in particular…

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

Let $(M^n, g)$ be a compact K\"ahler manifold with nonpositive bisectional curvature. We show that a finite cover is biholomorphic and isometric to a flat torus bundle over a compact K\"ahler manifold $N^k$ with $c_1 < 0$. This confirms a…

This paper is devoted to the classification of irregular surfaces of general type with $p_g=q=2$ and non birational bicanonical map. The main result is that, if $S$ is such a surface and if $S$ is minimal with no pencil of curves of genus…

Let X be a compact K\"ahler manifold such that the universal cover admits a compactification. We conjecture that the fundamental group is almost abelian and reduce it to a classical conjecture of Iitaka.

In this paper we classify the topological invariants of the possible branch loci of a smooth double cover $f:X\rightarrow Y$ of a K3 surface $Y$. We describe some geometric properties of $X$ which depend on the properties of the branch…

A compact complex manifold X is said to be rationally cohomologically rigidified if its automorphism group Aut(X) acts faithfully on the cohomology ring H*(X,Q). In this note, we prove that, surfaces of general type with irregularity q>2…

We construct an orientable ribbon surface F in B^4, which is universal in the following sense: any compact orientable pl 4-manifold having a handle decomposition with 0-, 1- and 2-handles can be represented as a cover of B^4 branched over…

Suppose $G$ is a connected complex Lie group and $\Gamma$ is a discrete subgroup such that $X := G/\Gamma$ is K\"ahler and the codimension of the top non--vanishing homology group of $X$ with coefficients in $\mathbb Z_2$ is less than or…