Related papers: Non-algebraic compact K\"ahler threefolds admittin…

We provide a clarification of the classification of two-dimensional algebras over an arbitrary base field. Using this clarification, we determine the number of non-isomorphic two-dimensional algebras over a finite field.

For a compact complex manifold, we introduce holomorphic foliations associated with certain abelian subgroups of the automorphism group. Such foliations are generalizations of holomorphic principal torus bundles. If there exists a…

In this article we show that if $(X, \Delta)$ is a log canonical compact K\"ahler $3$-fold such that $K_X+\Delta$ is nef and the numerical dimension $\nu(K_X+\Delta)\neq 2$, then $K_X+\Delta$ is semi-ample.

Classification results are given for (i) compact quaternionic K\"ahler manifolds with a cohomogeneity-one action of a semi-simple group, (ii) certain complete hyperK\"ahler manifolds with a cohomogeneity-two action of a semi-simple group…

We determine the Hodge endomorphism algebras of non-projective complex K3 surfaces (and more generally, hyperk\"ahler manifolds). We show that they are either totally real fields or number fields generated by Salem numbers. This is unlike…

We introduce the class of extended admissible groups, which include both fundamental groups of non-geometric 3-manifolds and Croke-Kleiner admissible groups. We show that the class of extended admissible groups is quasi-isometrically rigid.

We classify Q-Fano threefolds of Fano index > 2 and big degree.

(1) Every infinite, Abelian compact (Hausdorff) group K admits 2^|K|-many dense, non-Haar-measurable subgroups of cardinality |K|. When K is nonmetrizable, these may be chosen to be pseudocompact. (2) Every infinite Abelian group G admits a…

Simply connected compact K\"ahler manifolds of dimension up to three with elliptic homotopy type are characterized in terms of their Hodge diamonds. This is applied to classify the simply connected K\"ahler surfaces and Fano threefolds with…

We prove that every compact K\"ahler threefold $X$ of Kodaira dimension $\kappa = 0$ or $1$ has a $\mathbf{Q}$-factorial bimeromorphic model $X'$ with at worst terminal singularities such that for each curve $C \subset X'$, the pair…

The basic class of the non-integrable almost complex manifolds with Norden metric is considered. Its curvature properties are studied. The isotropic Kaehler type of investigated manifolds is introduced and characterized geometrically.

In this paper, we investigate automorphisms of compact K\"ahler manifolds with different levels of topological triviality. In particular, we provide several examples of smooth complex projective surfaces X whose groups of…

We determine normal forms of the multiplication of four-dimensional anti-commutative algebras over a field $\mathbb K$ of characteristic zero having an analogous family of flags of subalgebras as the four-dimensional non-Lie binary Lie…

Let S be a K3 surface that admits a non-symplectic automorphism $\rho$ of order 3. We divide $S\times \mathbb{P}^1$ by $\rho\times\psi$ where $\psi$ is an automorphism of order 3 of $\mathbb{P}^1$. There exists a threefold ramified cover of…

It is determined exactly which classifiable C*-algebras have approximately inner flip. The answer includes a number of C*-algebras with torsion in their K-theory, and a number of C*-algebras that are self-absorbing but not strongly…

We introduce a double complex that can be associated to certain Lie algebras, and show that its cohomology determines an obstruction to the existence of a half-flat SU(3)-structure. We obtain a classification of the 6-dimensional…

A classification theorem for nearly K\"ahler manifolds of constant antiholomorphic sectional curvature is proved.

The first example of a compact manifold admitting both complex and symplectic structures but not admitting a K\"ahler structure is the renowned Kodaira-Thurston manifold. We review its construction and show that this paradigm is very…

We show that there exists a non-K\"ahler Calabi-Yau fourfold, constructing an example by smoothing a normal crossing variety.

We classify K\"ahler-Einstein manifolds which admit a K\"ahler immersion into a finite dimensional complex projective space endowed with the Fubini-Study metric, whose codimention is not greater than 3 and whose metric is rotation…