Related papers: Fibered orbifolds and crystallographic groups, II

Let O be a compact orientable 3-orbifold with non-empty singular locus and a finite volume hyperbolic structure. (Equivalently, O is the quotient of hyperbolic 3-space by a lattice in PSL(2,C) with torsion.) Then we prove that O has a tower…

We explain the observation by Candelas and Font that the Dynkin diagrams of nonabelian gauge groups occurring in type IIA and F-theory can be read off from the polyhedron $\Delta^*$ that provides the toric description of the Calabi-Yau…

In the present paper we consider fibrations $f: S \ra B$ of an algebraic surface onto a curve $B$, with general fibre a curve of genus $g$. Our main results are: 1) A structure theorem for such fibrations in the case $g=2$ 2) A structure…

In this study, four-dimensional $N=1$ F-theory models with multiple U(1) gauge group factors are constructed. A class of rational elliptic 4-folds, which we call as "$\frac{1}{2}$Calabi-Yau 4-folds," is introduced, and we construct the…

We prove that a transversely holomorphic foliation which is transverse to the fibers of a fibration, is a Seifert fibration if the set of compact leaves is not of zero measure. Similarly, we prove that a finitely generated subgroup of…

We survey the existing parts of a classification of finite groups generated by orthogonal transformations in a finite-dimensional Euclidean space whose fixed point subspace has codimension one or two and extend it to a complete…

This paper is a detailed study of a class of isolated Gorenstein threefold singularities, called hyperconifolds, that are finite quotients of the conifold. First, it is shown that hyperconifold singularities arise naturally in limits of…

A very important class of homogeneous Riemannian manifolds are the so-called normal homogeneous spaces, which have associated a canonical connection. In this work we obtain geometrically the (connected component of the) group of affine…

We introduce a new category of non-archimedean analytic spaces over a complete discretely valued field. These spaces, which we call uniformly rigid, may be viewed as classical rigid-analytic spaces together with an additional uniform…

A geometric characterization of the structure of the group of automorphisms of an arbitrary Birkhoff-Grothendieck bundle splitting $\bigoplus_{i=1}^{r} \mathcal(m_{i})$ over $\mathbb{C}\mathbb{P}^{1}$ is provided, in terms of its action on…

This article is devoted to the investigation of wrap groups of connected fiber bundles over the fields of real $\bf R$, complex $\bf C$ numbers, the quaternion skew field $\bf H$ and the octonion algebra $\bf O$. These groups are…

Let (M,g) be a compact Riemannian manifold of dimension n. For k \in {0,...,n}, we denote Gr_{k}(M) the set of compact, connected and oriented submanifolds of M of dimension k. This set is called the non-linear Grassmannian. In this…

An algorithm to systematically construct all Calabi-Yau elliptic fibrations realized as hypersurfaces in a toric ambient space for a given base and gauge group is described. This general method is applied to the particular question of…

We discuss some aspects of F-theory in four dimensions on elliptically fibered Calabi-Yau fourfolds which are Calabi-Yau threefold fibrations. A particularly simple class of such manifolds emerges for fourfolds in which the generic…

Elliptic Calabi-Yau fibrations with Mordell-Weil group of rank two are constructed. Such geometries are the basis for F-theory compactifications with two abelian gauge groups in addition to non-abelian gauge symmetry. We present the…

In 2007 Agol showed that if N is an aspherical compact 3-manifold with empty or toroidal boundary such that its fundamental group is virtually RFRS, then $N$ is virtually fibered. We give a largely self-contained proof of Agol's theorem…

Let $Z$ be a Fano variety satisfying the condition that the rank of the Grothendieck group of $Z$ is one more than the dimension of $Z$. Let $\omega_Z$ denote the total space of the canonical line bundle of $Z$, considered as a non-compact…

We develop further our fibre bundle construct of non-commutative space-time on a Minkowski base space. We assume space-time is non-commutative due to the existence of additional non-commutative algebraic structure at each point x of…

We describe pairs (p,n) such that n-dimensional affine space is fibered by pairwise skew p-dimensional affine subspaces. The problem is closely related with the theorem of Adams on vector fields on spheres and the Hurwitz-Radon theory of…

We observe that any regular Lie groupoid G over an manifold M fits into an extension $K \to G \to E$ of a foliation groupoid E by a bundle of connected Lie groups K. If $\FF$ is the foliation on M given by the orbits of E and T is a…