Related papers: Virtually abelian K\"ahler and projective groups

We study meromorphic actions of unipotent complex Lie groups on compact K\"ahler manifolds using moment map techniques. We introduce natural stability conditions and show that sets of semistable points are Zariski-open and admit geometric…

Euler-symmetric projective varieties are nondegenerate projective varieties admitting many C*-actions of Euler type. They are quasi-homogeneous and uniquely determined by their fundamental forms at a general point. We show that…

We classify closed abelian subgroups of the automorphism group of any compact classical simple Lie algebra whose centralizer has the same dimension as the dimension of the subgroup, and describe Weyl groups of maximal abelian subgroups.

Given a complex manifold $X$, any K\"ahler class defines an affine bundle over $X$, and any K\"ahler form in the given class defines a totally real embedding of $X$ into this affine bundle. We formulate conditions under which the affine…

Let k be a field, and let {\pi}:\tilde{X} -> X be a proper birational morphism of irreducible k-varieties, where \tilde{X} is smooth and X has at worst quotient singularities. When the characteristic of k is zero, a theorem of Koll\'ar in…

We introduce the notion of (twisted) quiver representations in abelian categories and study the category of such representations. We construct standard resolutions and coresolutions of quiver representations and study basic homological…

It was recently proven that all free and many virtually free verbally closed subgroups are algebraically closed in any group. We establish sufficient conditions for a group that is an extension of a free non-abelian group by a group…

We consider the class of quasiprojective varieties admitting a dominant morphism onto a curve with negative Euler characteristic. The existence of such a morphism is a property of the fundamental group. We show that for a variety in this…

We study the quantization of spaces whose K-theory in the classical limit is the ring of dual numbers $\mathbb{Z}[t]/(t^2)$. For a compact Hausdorff space we recall necessary and sufficient conditions for this to hold. For a compact quantum…

In this note, we show that the cohomology groups of (virtually) nilpotent K\"ahler groups are naturally endowed with a mixed Hodge structure. These structures make the Hopf morphisms into mixed Hodge structures morphisms. We illustrate this…

We give an equivalent definition of compact locally conformally hyperk\"ahler manifolds in terms of the existence of a nondegenerate complex two-form with natural properties. This is a conformal analogue of Beauville's theorem stating that…

We show that a complex structure on a nilpotent almost abelian real Lie algebra is unique if it exists. As a consequence, we get full control over the cohomology and deformations of almost abelian complex nilmanifolds.

In Kaehler manifolds are investigated conformally flat totally real submanifolds, which are semiparallel or have semiparallel mean curvature vector.

In the paper we prove a factorization theorem for representations of fundamental groups of compact K\"{a}hler manifolds ({\em K\"{a}hler groups}) into solvable matrix groups. We apply this result to prove that the universal covering of a…

We introduce and motivate the definition of the virtual Rokhlin property for topological groups. We then classify the 2-manifolds whose homeomorphism groups have the virtual Rokhlin property. We also establish the analogous result for…

An almost K\"ahler structure is {\it extremal} if the Hermitian scalar curvature is a Killing potential [29]. When the almost complex structure is integrable it coincides with extremal K\"ahler metric in the sense of Calabi [8]. We observe…

Let K be a Cantor set embedded in the real line R. Following Funar and Neretin, we define the diffeomorphism group of K as the group of homeomorphisms of K which locally look like a diffeomorphism between two intervals of R.…

In this paper we showed that every connected extremal K\"ahler submanifold of a complex projetive space has a natural extension which is a complete K\"ahler manifold and admits a holomorphic isometric immersion into the same ambient space.…

It is well-known that random groups with at least as many relators as generators have vanishing first betti number with high probability. In this paper we extend this question and study maps from few-relators random groups to infinite…

We prove that a finitely generated group contains a sequence of non-trivial elements which converge to the identity in every compact homomorphic image if and only if the group is not virtually abelian.