Related papers: Orbifold modifications of complex analytic spaces

Chen and Ruan's orbifold cohomology of the symmetric product of a complex manifold is calculated. An isomorphism of rings (up to a change of signs) $H_{orb}^*(X^n/S_n;\complex) \cong H^*(X^{[n]};\complex)$ between the orbifold cohomology of…

Given a compact metric space $X$, we associate to it an inverse sequence of finite $T_0$ topological spaces. The inverse limit of this inverse sequence contains a homeomorphic copy of $X$ that is a strong deformation retract. We provide a…

We show that the set of points of an overt closed subspace of a metric completion of a Bishop-locally compact metric space is located. Consequently, if the subspace is, moreover, compact, then its collection of points is Bishop compact.

We first notice in this article that if a compact K\"{a}hler manifold has the same integral cohomology ring and Pontrjagin classes as the complex projective space $\mathbb{C}P^n$, then it is biholomorphic to $\mathbb{C}P^n$ provided $n$ is…

We say that a complex analytic space, $X$, is an intersection cohomology manifold if and only if the shifted constant sheaf on $X$ is isomorphic to intersection cohomology; this is quickly seen to be equivalent to $X$ being a homology…

In this short Note we show that the direct image sheaf R 1 $\pi$ * (O X) associated to an analytic family of compact complex manifolds $\pi$ : X $\rightarrow$ S parametrized by a reduced complex space S is a locally free (coherent) sheaf of…

Let $X$ be an algebraic variety over $\mathbf{C}$. We define a canonical compactification $X^{\!\urcorner}$ of the complex analytic space $X(\mathbf{C})$ by adding a Berkovich space over a trivially valued field at the boundary. The…

For pointed compact metric spaces $(X,d)$, we address the biduality problem as to when the space of Lipschitz functions $\mathrm{Lip}_0(X,d)$ is isometrically isomorphic to the bidual of the space of little Lipschitz functions…

Using examples of compact complex 3-manifolds which arise as twistor spaces, we show that the class of compact complex manifolds bimeromorphic to K\"ahler manifolds is not stable under small deformations of complex structure.

We describe a geometric compactification of the moduli stack of left invariant complex structures on a fixed real Lie group or a fixed quotient. The extra points are CR structures transverse to a real foliation.

This paper examines the existence and region of convergence of Fourier transform of the functions of bicomplex variables with the help of projection on its idempotent components as auxiliary complex planes. Several basic properties of this…

Let $M$ be a compact complex manifold equipped with a hyperk\"ahler metric, and $X$ be a closed complex analytic subvariety of $M$. In alg-geom/9403006, we proved that $X$ is trianalytic, i. e., complex analytic with respect to all complex…

Consider a connected manifold of dimension at least two and the group of compactly supported diffeomorphisms that are compactly supported isotopic to the identity. This group acts $n$-transitive: Any tuple of $n$ points can be moved to any…

Let k be a complete, non-Archimedean field and let X be a k-analytic space ; assume that there exists a tamely ramified finite extension L/k such that X_L is isomorphic to an open polydisc over L ; we prove that X is itself isomorphic to an…

We prove the following result: Let $(M,g_0)$ be a compact manifold of dimension $n\geq 12$ with positive isotropic curvature. Then $M$ is diffeomorphic to a spherical space form, or the total space of an orbifiber bundle over $\mathbb{S}^1$…

In this paper, we try to generalize to the case of compact Riemannian orbifolds $Q$ some classical results about the existence of closed geodesics of positive length on compact Riemannian manifolds $M$. We shall also consider the problem of…

We study the analytic torsion of odd-dimensional hyperbolic orbifolds $\Gamma \backslash \mathbb{H}^{2n+1}$, depending on a representation of $\Gamma$. Our main goal is to understand the asymptotic behavior of the analytic torsion with…

We recall the complex structure on the generalised loop spaces $W^{k,2}(S,X)$, where $S$ is a compact real manifold with boundary and $X$ is a complex manifold, and prove a Hartogs-type extension theorem for holomorphic maps from certain…

We study isometric circle actions on 7 dimensional positively curved Eschenburg spaces which are almost free, thus giving rise to orbifold fibrations of these spaces. This shows in particular that every known example of compact manifolds…

We prove that the stable manifold of every point in a compact hyperbolic invariant set of a holomorphic automorphism of a complex manifold is biholomorphic to a complex vector space, provided that a bunching condition, which is weaker than…