Related papers: Blowing up generalized Kahler 4-manifolds

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…

In this article we introduce the notion of Polyhedral Kahler manifolds, even dimensional polyhedral manifolds with unitary holonomy. We concentrate on the 4-dimensional case, prove that such manifolds are smooth complex surfaces, and…

We deal with compact Kaehler manifolds M which are acted on by a semisimple compact Lie group G of isometries with codimension one regular orbits. We provide an explicit description of the standard blow-ups of such manifolds along complex…

An asymptotic formula for the Tian-Paul CM-line of a flat family blown-up at a flat closed sub-scheme is given. As an application we prove that the blow-up of a polarized manifold along a (relatively) Chow-unstable submanifold admits no…

Generalized Kahler geometry is the natural analogue of Kahler geometry, in the context of generalized complex geometry. Just as we may require a complex structure to be compatible with a Riemannian metric in a way which gives rise to a…

We give an elementary proof of the fact that any 4-dimensional para-Hermitian manifold admits a unique para-Kaehler--Weyl structure. We then use analytic continuation to pass from the para-complex to the complex setting and thereby show any…

Let $(M,J)$ be a $2n$-dimensional almost complex manifold and let $x\in M$. We define the notion of almost complex blow-up of $(M,J)$ at $x$. We prove the existence of almost complex blow-ups at $x$ under suitable assumptions on the almost…

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…

We introduce K-deformations of generalized complex structures on a compact Kahler manifold $M=(X, J)$ with an effective anti-canonical divisor and show that obstructions to K-deformations of generalized complex structures on $M$ always…

Let $M$ be a real-analytic connected CR-hypersurface of CR-dimension $n>0$ having a point of Levi-nondegeneracy. The following alternative is demonstrated for both the symmetry algebra $s$ and the automorphism group $G$ of $M$. Denote by…

We show that if $(M,\omega)$ is any compact K\"ahler manifold, then the blowup of $M$ at any point furnishes a K\"ahler metric with scalar curvature globally and arbitrarily $C^0$-close to the scalar curvature of $\omega$. It follows that…

A complex ruled surface admits an iterated blow-up encoded by a parabolic structure with rational weights. Under a condition of parabolic stability, one can construct a Kaehler metric of constant scalar curvature on the blow-up according to…

A Riemannian metric on a compact 4-manifold is said to be Bach-flat if it is a critical point for the L2-norm of the Weyl curvature. When the Riemannian 4-manifold in question is a Kaehler surface, we provide a rough classification of…

We obtain topological obstructions to the existence of a complete Riemannian metric with uniformly positive scalar curvature on certain (non-compact) $4$-manifolds. In particular, such a metric on the interior of a compact contractible…

We construct a generalization of twistor spaces of hypercomplex manifolds and hyper-Kahler manifolds $M$, by generalizing the twistor $\mathbb{P}^{1}$ to a more general complex manifold $Q$. The resulting manifold $X$ is complex if and only…

We investigate the collapsing geometry of hyperk\"ahler 4-manifolds. As applications we prove two well-known conjectures in the field. (1) Any collapsed limit of unit-diameter hyperk\"ahler metrics on the K3 manifold is isometric to one of…

The paper is devoted to the investigation of four-dimensional Kahler manifolds admitting non-affine H-projective mappings. We find all such manifolds which are non-Einstein. In the paper also Kahler manifolds admitting infinitesimal…

We prove that the generalized rational blowdown, a surgery on smooth 4-manifolds, can be performed in the symplectic category.

Real blow-up, including inhomogeneous versions, of boundary faces of a manifold (with corners) is an important tool for resolving singularities, degeneracies and competing notions of homogeneity. These constructions are shown to be…

In this paper we present a method for extending the blowup method, in the formulation of Krupa and Szmolyan, to flat slow manifolds that lose hyperbolicity beyond any algebraic order. Although these manifolds have infinite co-dimension,…