Related papers: Finite-volume hyperbolic Coxeter 4-dimensional pol…

In this paper, we prove the Bounded Height Conjecture which the author formulated in [2]. As a corollary, it follows that there are only a finite number of hyperbolic three manifolds of bounded volume and trace field degree.

We characterise Newton polytopes of nondegenerate quadratic forms and Newton polyhedra of Morse singularities.

We construct a 2-parameter family of 4-dimensional polytopes with extreme combinatorial structure: In this family, the ``fatness'' of the f-vector gets arbitrarily close to 9, the ``complexity'' (given by the flag vector) gets arbitrarily…

We obtain a complete classification of complex Kobayashi-hyperbolic manifolds of dimension $n\ge 2$, for which the dimension of the group of holomorphic automorphisms is equal to $n^2$.

We prove that the Fuchsian (4,4,4) triangle group and also right-angled reflection groups of hyperbolic spaces in higher dimensions admit ergodic invariant random subgroups having uncountably many isomorphism types of subgroups in their…

We investigate representations of Coxeter groups into $\mathrm{GL}(n,\mathbb{R})$ as geometric reflection groups which are convex cocompact in the projective space $\mathbb{P}(\mathbb{R}^n)$. We characterize which Coxeter groups admit such…

A three-dimensional orthoscheme is defined as a tetrahedron whose base is a right-angled triangle and an edge joining the apex and a non-right-angled vertex is perpendicular to the base. A generalization, called complete orthoschemes, of…

We show that if M is a complete, finite-volume, hyperbolic 3-manifold having exactly one cusp, and if H_1(M;Z_2) has dimension at least 6, then M has volume greater than 5.06. We also show that if M is a closed, orientable hyperbolic…

We describe the optimal horoball packings of asymptotic Koszul type Coxeter simplex tilings of $5$-dimensional hyperbolic space where the symmetries of the packings are generated by Coxeter groups. We find that the optimal horoball packing…

The goal of this paper is to study the geometry of cusped complex hyperbolic manifolds through their compactifications. We characterize toroidal compactifications with non-nef canonical divisor. We derive effective very ampleness results…

This paper is subsequent to [5]. In this paper, we extend the classification of hyperbolic Dehn fillings with sufficiently large coefficients by addressing the remaining case not covered in [5]. Specifically, by considering the case in…

This paper is an introduction to Coxeter polyhedra in spherical, Euclidean, and hyperbolic geometries. It consists of essentially two parts that could be read independently. In the first we introduce non-obtuse polyhedra in the spherical,…

The article [14] gives a list of 51 symplectic hypergeometric monodromy groups corresponding to primitive pairs of degree four polynomials, which are products of cyclotomic polynomials, and for which, the absolute value of the leading…

A compact hyperbolic "cobweb" manifold (hyperbolic space form) of symbol $Cw(6,6,6)$ will be constructed in Fig.1,4,5 as a representant of a presumably infinite series $Cw(2p,2p,2p)$ $(3 \le p \in \bN$ natural numbers). This is a by-product…

In this note we prove that the number of combinatorial types of $d$-polytopes with $d+1+\alpha$ vertices and $d+1+\beta$ facets is bounded by a constant independent of $d$.

Atkinson [2] found a sequence of three-dimensional hyperbolic polyhedra whose dihedral angles are $\pi /3$. In this paper, we construct another sequence of such polyhedra. We also determine the volumes of some of these polyhedra.

In this article we study homotopes of finite-dimensional algebras (not necessarily, associative). In the case of associative algebras we study homotopes by methods of Category theory and give description of so-called well-tempered elements…

This note surveys recent progress toward the profinite rigidity of orientable finite-volume hyperbolic 3-manifolds. Beginning in a brief review of some basic settings of profinite completion and rigidity of general groups, we state the…

Let X be a complex, Gorenstein, Q-factorial, toric Fano variety. We prove two conjectures on the maximal Picard number of X in terms of its dimension and its pseudo-index, and characterize the boundary cases. Equivalently, we determine the…

We construct a hyperbolic three-manifold with trivial finite type invariants up to a given degree.