Related papers: Non-K\"ahler complex structures on $R^4$ II

In this paper I construct, using off the shelf components, a compact symplectic manifold with a non-trivial Hamiltonian circle action that admits no Kaehler structure. The non-triviality of the action is guaranteed by the existence of an…

In this paper, we build a compactification by a strictly pseudoconvex CR structure for complete and non-compact K\"ahler manifolds whose curvature tensor is asymptotic to that of the complex hyperbolic space.

In this paper we describe the construction of a new class of non-K\"ahler compact complex manifolds. They can be seen as a generalization of Sankaran, OT and LVMB manifolds. Moreover, we give properties of these new spaces. Their Kodaira…

We prove that all minimal symplectic four-manifolds are essentially irreducible. We also clarify the relationship between holomorphic and symplectic minimality of K\"ahler surfaces. This leads to a new proof of the deformation-invariance of…

Using the theory of totally real number fields we construct a new class of compact complex non-K{\"a}hler manifolds in every even complex dimension and study their analytic and geometric properties.

We construct noncomplex smooth 4-manifolds which admit genus-2 Lefschetz fibrations over S^2. The fibrations are necessarily hyperelliptic, and the resulting 4-manifolds are not even homotopy equivalent to complex surfaces. Furthermore,…

In continuation of our paper in Math. Ann. 333 we classify smooth complex projective threefolds X with -K_X big and nef but not ample and Picard number 2, whose anticanonical map is small. We assume also that the Mori contraction of X and…

We study restrictions on cohomology algebras of Kaehler compact manifolds, not depending on the h^{p,q} numbers or the symplectic structure. To illustrate the effectiveness of these restrictions, we give a number of examples of compact…

The paper is part of an attempt of understanding non-K\"ahler threefolds. We start by looking at compact complex non-K\"ahler threefolds with algebraic dimension two and admitting locally conformally K\"ahler metrics. Under certain…

We present some families of cubic hypersurfaces in $\mathbb P^5 (\mathbb C)$ containing a plane whose associated quadric bundle does not have a rational section.

Let (J,g) be a Hermitian structure on a compact nilmanifold M with invariant complex structure J and compatible metric g, which is not required to be invariant. We give classifications of 6-dimensional nilmanifolds M admitting strong…

The coadjoint orbits of compact Lie groups each carry a canonical (positive definite) K\"ahler structure, famously used to realize the group's irreducible representations in holomorphic sections of appropriate line bundles (Borel-Weil…

We investigate the $\mathrm{Pin}^-(2)$-monopole invariants of symplectic $4$-manifolds and K\"{a}hler surfaces with real structures. We prove the nonvanishing theorem for real symplectic $4$-manifolds which is an analogue of Taubes'…

We introduce a new generalization of Gompf nuclei and give applications. We construct infinitely many exotic smooth structures for a large class of compact 4-manifolds with boundary, regarding topological invariants. We prove that a large…

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…

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 study smooth proper embeddings of compact orientable surfaces in compact orientable $4$-manifolds and elements in the mapping class group of that surface which are induced by diffeomorphisms of the ambient $4$-manifolds. We call such…

Let $S^n(X)$ be the $n$-fold symmetric product of a compact connected Riemann surface $X$ of genus $g$ and gonality $d$. We prove that $S^n(X)$ admits a K\"ahler structure such that all the holomorphic bisectional curvatures are nonpositive…

We introduce the concept of Spin^G-structure in a SO-bundle, where $G\subset U(V)$ is a compact Lie group containing $-id_V$. We study and classify $Spin^G(4)$-structures on 4-manifolds, we introduce the G-Monopole equations associated with…

We study generalized Kaehler manifolds for which the corresponding complex structures commute and classify completely the compact generalized Kaehler four-manifolds for which the induced complex structures yield opposite orientations.