Related papers: A characterization of surfaces whose universal cov…

In this paper, we show that if $X$ is a smooth variety of general type of dimension $m \geq 2$, for which its canonical map induces a double cover onto $Y$, where $Y$ is a projective bundle over $\mathbf P^1$, or onto a projective space or…

We prove that there exists a 1-convex surface whose universal covering does not satisfy the discrete disk property.

We prove that any nilpotent regular covering over a compact K\"ahler surface is holomorphically convex if it does not have two ends. Furthermore, we show that the Malcev covering of any compact K\"ahler manifold has at most one end.

A unimodular complex surface is a complex 2-manifold X endowed with a holomorphic volume form. A strictly pseudoconvex real hypersurface M in X inherits not only a CR-structure but a canonical coframing as well. In this article, this…

We prove that every Kaehler solvmanifold has a finite covering whose holomorphic reduction is a principal bundle. An example is given that illustrates the necessity, in general, of passing to a proper covering. We also answer a stronger…

A planar set $P$ is said to be cover-decomposable if there is a constant $k=k(P)$ such that every $k$-fold covering of the plane with translates of $P$ can be decomposed into two coverings. It is known that open convex polygons are…

For a closed oriented surface $ \Sigma $ we define its degenerations into singular surfaces that are locally homeomorphic to wedges of disks. Let $X_{\Sigma,n}$ be the set of isomorphism classes of orientation preserving $n$-fold branched…

We prove that the surface $S(X)$ of bitangent lines of a general smooth quartic surface $X$ in $\mP^3$ has unobstructed deformations of dimension $20=h^1(S(X), T_{S(X)})$. In addition, we show that the space of infinitesimal embedded…

Finite-sheeted covering mappings onto compact connected groups are studied. It is shown that a finite-sheeted covering mapping from a connected Hausdorff topological space onto a compact connected abelian group G must be a homeomorphism…

In this paper we prove that the universal cover of a smooth projective variety with nilpotent fundamental group is holomorphically convex.

Let $(X, \Delta)$ be a compact K\"ahler klt pair, where $K_X + \Delta$ is ample or numerically trivial, and $\Delta$ has standard coefficients. We show that if equality holds in the orbifold Miyaoka-Yau inequality for $(X, \Delta)$, then…

We consider minimal compact complex surfaces S with Betti numbers b_1=1 and n=b_2>0. A theorem of Donaldson gives n exceptional line bundles. We prove that if in a deformation, these line bundles have sections, S is a degeneration of…

Let $X$ be a compact Riemann surface of genus $\geq 2$ of constant negative curvature -1. An extremal disk is an embedded (resp. covering) disk of maximal (resp. minimal) radius. A surface containing an extremal disk is an {\em extremal…

In this paper, we prove the irreducibility of the monodromy action on the anti-invariant part of the vanishing cohomology on a double cover of a very general element in an ample hypersurface of a complex smooth projective variety branched…

We show that a compact complex surface which admits a conformally K\"ahler metric g of positive orthogonal holomorphic bisectional curvature is biholomorphic to the complex projective plane. In addition, if g is a Hermitian metric which is…

Let X be a smooth cubic hypersurface. We prove that a general cubic surface is isomorphic to a hyperplane section of X .

Let $O$ be a nilpotent orbit of a complex semisimple Lie algebra $\mathfrak{g}$ and let $\pi: X \to \bar{O}$ be the finite covering associated with the universal covering of $O$. In the previous article we have explicitly constructed a…

In this paper, we study biharmonic hypersurfaces in Einstein manifolds. Then, we determine all the biharmonic hypersurfaces in irreducible symmetric spaces of compact type which are regular orbits of commutative Hermann actions of…

Every normal complex surface singularity with $\mathbb Q$-homology sphere link has a universal abelian cover. It has been conjectured by Neumann and Wahl that the universal abelian cover of a rational or minimally elliptic singularity is a…

In the first part of the paper we associate a pre-additive category $\mathcal{C}(\Sigma)$ to a closed oriented surface $\Sigma$, called the {\em contact category} and constructed from contact structures on $\Sigma\times[0,1]$. There are…