Related papers: K\"ahler groups and subdirect products of surface …

We introduce a new class of Abelian groups which lies strictly between the classes of co-Hopfian groups and Dedekind-finite groups, calling these groups {\it Bassian-finite}. We prove the surprising fact that in the torsion case the…

For any elliptic K3 surface $\mathfrak{F}: \mathcal{K} \rightarrow \mathbb{P}^1$, we construct a family of collapsing Ricci-flat K\"ahler metrics such that curvatures are uniformly bounded away from singular fibers, and which…

We introduce some special presentations on finite groups, that we call "diagonal double Kodaira structures" and whose existence is equivalent to the existence of some special Kodaira fibred surfaces, that we call "diagonal double Kodaira…

We describe the supercharacter theories of the semidirect product of H and K, $H\rtimes K$ in terms of the supercharacter theories of the direct product of H and K in the case when both H and K are Abelian groups. To do this we introduce…

We construct large families of new collapsing hyperk\"ahler metrics on the K3 surface. The limit space is the quotient of a flat 3-torus by an involution. Away from finitely many exceptional points the collapse occurs with bounded…

Let $X$ be a compact K\"ahler space with klt singularities and vanishing first Chern class. We prove the Bochner principle for holomorphic tensors on the smooth locus of $X$: any such tensor is parallel with respect to the singular…

Let X be a compact K\"ahler manifold such that the universal cover admits a compactification. We conjecture that the fundamental group is almost abelian and reduce it to a classical conjecture of Iitaka.

The kernel of the natural projection of a graph product of groups onto their direct product is called the Cartesian subgroup of the graph product. This construction generalises commutator subgroups of right-angled Coxeter and Artin groups.…

This paper concerns the explicit construction of extremal Kaehler metrics on total spaces of projective bundles, which have been studied in many places. We present a unified approach, motivated by the theory of hamiltonian 2-forms (as…

The Torelli group of a compact non-orientable Klein surface is the subgroup of the modular group consisting of the mapping classes that act trivially on the first homology group of the surface. We prove that if a surface has genus at least…

Let $\mathcal{X}_S$ denote the class of spaces homeomorphic to two closed orientable surfaces of genus greater than one identified to each other along an essential simple closed curve in each surface. Let $\mathcal{C}_S$ denote the set of…

We study finite abelian groups acting on three-dimensional rationally connected varieties. We concentrate on the groups of K3 type, that is, abelian extensions by a cyclic group of groups that faithfully act on a K3 surface. In particular,…

In this paper we deal with a new class of Clifford algebra valued automorphic forms on arithmetic subgroups of the Ahlfors-Vahlen group. The forms that we consider are in the kernel of the operator $D \Delta^{k/2}$ for some even $k \in…

Given any connected topological space $X$, assume that there exists an epimorphism $\phi: \pi_1(X) \to \mathbb{Z}$. The deck transformation group $\mathbb{Z}$ acts on the associated infinite cyclic cover $X^\phi$ of $X$, hence on the…

In this paper, a construction of an infinite dimensional associative algebra, which will be called a \emph{Surface Algebra}, is associated in a "canonical" way to a dessin d'enfant, or more generally, a cellularly embedded graph in a…

We study invariant pseudo-K\"ahler structures on a solvmanifold $G$ such that the Lie algebra $\mathfrak{g}$ is almost abelian, that is $\mathfrak{g}=\mathfrak{h}\rtimes\mathbb{R}$, with $\mathfrak{h}$ abelian; comparing with the…

We prove that a hyper-K\"ahler fourfold satisfying a mild topological assumption is of K3$^{[2]}$ deformation type. This proves in particular a conjecture of O'Grady stating that hyper-K\"ahler fourfolds of K3$^{[2]}$ numerical type are of…

We build actions of Thompson group V (related to the Cantor set) and of the so-called "spheromorphism" group of Neretin, on "towers" of moduli spaces of genus zero real stable curves. The latter consist of inductive limits of spaces which…

We explicitly construct new subgroups of the mapping class groups of an uncountable collection of infinite-type surfaces, including, but not limited to, free groups, Baumslag-Solitar groups, mapping class groups of other surfaces, and a…

We construct nontrivial homomorphisms from the quasi group of some cubic surfaces over $\bbF_{\!p}$ into a group. We show experimentally that the homomorphisms constructed are the only possible ones and that there are no nontrivial…