Related papers: Compact complex manifolds whose complement of an a…

We propose a class of N=2 supersymmetric nonlinear sigma models on the noncompact Ricci-flat Kahler manifolds, interpreted as the complex line bundles over the hermitian symmetric spaces. Kahler potentials and Ricci-flat metrics for these…

In this note we present, for every $n \geq 4$, a non-K\"ahler compact complex manifold $X$ of complex dimension $n$ admitting a balanced metric and an astheno-K\"ahler metric which is in addition $k$-th Gauduchon for any $1\leq k\leq n-1$.

This work establishes a structure theorem for compact K\"ahler manifolds with semipositive anticanonical bundle. Up to finite \'etale cover, it is proved that such manifolds split holomorphically and isometrically as a product of Ricci flat…

Among other things, we show that the ideal sheaf of a complex Hilbert submanifold of a pseudoconvex open subset of Hilbert space is acyclic over the ambient pseudoconvex open set. We also prove a vanishing theorem for a fairly general class…

A Dirac-type operator on a complete Riemannian manifold is of Callias-type if its square is a Schr\"{o}dinger-type operator with a potential uniformly positive outside of a compact set. We develop the theory of Callias-type operators…

On a complex manifold an Hermitian metric which is simultaneously SKT and balanced has to be necessarily K\"ahler. It has been conjectured that if a compact complex manifold (M,J) has an SKT metric and a balanced metric both compatible with…

Given a compact Kahler manifold with an extremal metric (M,\omega), we give sufficient conditions on finite sets points p_1,...,p_n and weights a_1,...a_n for which the blow up of M at p_1,...,p_n has an extremal metric in the Kahler class…

We define an analytic index and prove a topological index theorem for a non-compact manifold $M\_0$ with poly-cylindrical ends. We prove that an elliptic operator $P$ on $M\_0$ has an invertible perturbation $P+R$ by a lower order operator…

Let $M$ be a compact hyperkaehler manifold. The hyperkaehler structure equips $M$ with a set $R$ of complex structures parametrized by $CP^1$, called "the set of induced complex structures". It was known previously that induced complex…

We study the behaviour of families of Ricci-flat Kahler metrics on a projective Calabi-Yau manifold when the Kahler classes degenerate to the boundary of the ample cone. We prove that if the limit class is big and nef the Ricci-flat metrics…

This article finds constant scalar curvature Kahler metrics on certain compact complex surfaces. The surfaces considered are those admitting a holomorphic submersion to a curve, with fibres of genus at least 2. The proof is via an adiabatic…

To define a consistent perturbative geometric heterotic compactification the bundle is required to satisfy a subtle constraint known as ``stability,'' which depends upon the Kahler form. This dependence upon the Kahler form is highly…

We obtain an embedding theorem for compact strongly pseudoconvex CR manifolds which are bounadries of some complete Hermitian manifolds. We use this to compactify some negatively curved Kaehler manifolds with compact strongly pseudoconvex…

Suppose $G$ is a connected complex Lie group and $H$ is a closed complex subgroup such that $X := G/H$ is Kaehler and the codimension of the top non-vanishing homology group of $X$ with coefficients in $\mathbb Z_2$ is less than or equal to…

In this work, we will verify some comparison results on Kahler manifolds. They are complex Hessian comparison for the distance function from a closed complex submanifold of a Kahler manifold with holomorphic bisectional curvature bounded…

Let a torus $T$ act on a symplectic manifold $(M,\omega)$ with moment map $\phi$. We say that the Hamiltonian $T$-manifold $(M,\omega,\phi)$ has complexity one if $\frac{1}{2} \dim M - \dim T = 1$, and that it is K\"ahler if it admits an…

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 a classical result, due to F. Tricceri, that the blow-up of a manifold of locally conformally K\"ahler (l.c.K. for short) type at some point is again of l.c.K. type. However, the proof given in \cite{Tric} is somehow unclear. We give…

We consider complex manifolds that admit actions by holomorphic transformations of classical simple real Lie groups and classify all such manifolds in a natural situation. Under our assumptions, which require the group at hand to be…

In this paper, we consider a proper modification $f : \tilde M \to M$ between complex manifolds, and study when a generalized $p-$K\"ahler property goes back from $M$ to $\tilde M$. When $f$ is the blow-up at a point, every generalized…