Related papers: Oriented and Non-oriented Cubical Surfaces in The …
By a K3-surface with nine cusps I mean a compact complex surface with nine isolated double points $A_2$, but otherwise smooth, such that its minimal desingularisation is a K3-surface. In an earlier paper I showd that each such surface is a…
We systematically investigate properties of various triangle centers (such as orthocenter or incenter) located on the four faces of a tetrahedron. For each of six types of tetrahedra, we examine over 100 centers located on the four faces of…
We present a computational study of smooth curves of degree six in the real projective plane. In the Rokhlin-Nikulin classification, there are 56 topological types, refined into 64 rigid isotopy classes. We developed software that…
In this article we present theoretical and computational results on the existence of polyhedral embeddings of graphs. The emphasis is on cubic graphs. We also describe an efficient algorithm to compute all polyhedral embeddings of a given…
There exist cubical transition systems containing cubes having an arbitrarily large number of faces. A regular transition system is a cubical transition system such that each cube has the good number of faces. The categorical and…
A unique sink orientation (USO) is an orientation of the $n$-dimensional cube graph ($n$-cube) such that every face (subcube) has a unique sink. The number of unique sink orientations is $n^{\Theta(2^n)}$. If a cube orientation is not a…
The trigonal curves of genus 5 can be represented by projective plane quintics that have 1 singularity of delta invariant 1. Combining this with a partial sieve method for plane curves we count the number of such curves over any finite…
Any convex polytope whose combinatorial automorphism group has two orbits on the flags is isomorphic to one whose group of Euclidean symmetries has two orbits on the flags (equivalently, to one whose automorphism group and symmetry group…
In the context of non-abelian gerbes we define a cubical version of categorical group 2-bundles with connection over a smooth manifold. We define their two-dimensional parallel transport, study its properties, and define non-abelian Wilson…
This article investigates the subject of rigid compact complex manifolds. First of all we investigate the different notions of rigidity (local rigidity, global rigidity, infinitesimal rigidity, etale rigidity and strong rigidity) and the…
We show that any codimension one hyperbolic attractor of a diffeomorphism of a (d+1)-dimensional closed manifold is shape equivalent to a (d+1)-dimensional torus with a finite number of points removed, or, in the non-orientable case, to a…
A natural family of affine cubic surfaces arises from SL(2)-characters of the 4-holed sphere and the 1-holed torus. The ideal locus is a tritangent plane which is generic in the sense that the cubic curve at infinity consists of three lines…
We study geodesics on the Necker cube surface, $\mathbf N$, an infinite periodic Euclidean cone surface that is homeomorphic to the plane and is tiled by squares meeting three or six to a vertex. We ask: When does a geodesic on the surface…
A complex compact surface which carries an automorphism of positive topological entropy has been proved by Cantat to be either a torus, a K3 surface, an Enriques surface or a rational surface. Automorphisms of rational surfaces are quite…
A famous configuration of 27 lines on a non-singular cubic surface in $\mathbb P^3$ contains remarkable subconfigurations, and in particular the ones formed by six pairwise disjoint lines. We study such six-line configurations in the case…
Spin networks are graphs derived from 3nj symbols of angular momentum. The surface embedding, the topology and dualization of these networks are considered. Embeddings into compact surfaces include the orientable sphere S^2 and the torus T,…
We prove the 2-torus $\mathbb T$, an abelian linear algebraic group, is a fine moduli space of labeled, oriented, possibly-degenerate inscribable similarity classes of triangles, where a triangle is {\it inscribable} if it can be inscribed…
Compact polyhedra of cubic point symmetry Oh, exhibit surfaces of planar sections (facets) characterized by normal vector families {abc} with up to 48 members each, compatible with Oh symmetry. We focus first on polyhedra confined by facets…
The paper discusses the classification of surfaces of degree 10 and sectional genus 9 and 10. The surfaces of degree at most 9 are described through classical work dating from the last century up to recent years, while surfaces of degree 10…
We define an 'oriented convex region' as a convex region with a direction of symmetry. An earlier article had touched upon isosceles triangles, rectangles and ellipses. Here, we examine some more possible oriented containers - semicircles,…