Related papers: Moufang loops and toric surfaces
We survey some results on toric topology.
We give an interpretation of the construction of torsors from preceding work (Bertram, Kinyon: Associative Geometries. I, J. Lie Theory 20) in terms of classical projective geometry. For the Desarguesian case, this leads to a reformulation…
We present a notion of a random toric surface modeled on a notion of a random graph. We then study some threshold phenomena related to the smoothness of the resulting surfaces.
We study toric varieties over an arbitrary field with an emphasis on toric surfaces in the Merkurjev-Panin motivic category of "K-motives". We explore the decomposition of certain toric varieties as K-motives into products of central simple…
We survey some results on real rational surfaces focused on their topology and their birational geometry.
We consider two natural Lagrangian intersection problems in the context of symplectic toric manifolds: displaceability of torus orbits and of a torus orbit with the real part of the toric manifold. Our remarks address the fact that one can…
We investigate the problem of defining group or loop structures on spheres, where by ''sphere'' we mean the level set q(x) = c of a general K-valued quadratic form q, for an invertible scalar c. When K is a field and q non-degenerate, then…
We generalize an inequality for convex lattice polygons -- aka toric surfaces -- to general rational surfaces.
We investigate slice-quaternionic Hopf surfaces. In particular, we construct new structures of slice-quaternionic manifold on $\mathbb{S}^1\times\mathbb{S}^7$, we study their group of automorphisms and their deformations.
We study the equations of universal torsors on rational surfaces.
The main results of A. Zorich and I. Dynnikov about plane sections of periodic surfaces are extended to the PL case. As an application, the Stereographic Map of a truncated octahedron, extended to the whole $\Rt$ by periodicity, is analyzed…
We propose some problems on the classification of toric manifolds from the viewpoint of topology and survey related results.
Some elementary considerations are presented concerning Catenoids and their stability, separable minimal hypersurfaces, minimal surfaces obtainable by rotating shapes, determinantal varieties, minimal tori in S3, the minimality in Rnk of…
We discuss methods to construct a polynomial parametrization of some interesting knotted surfaces (knotted spheres, knotted tori and knotted planes) and provide examples.
Reconstruction theorem for the Moufang loops is proved.
Concept of a birepresentation for the Moufang loops is elaborated.
We classify 1-dimensional connected dually flat manifolds $M$ that are toric in the sense of [Molitor, arXiv:2109.04839], and show that the corresponding torifications are complex space forms. Special emphasis is put on the case where M is…
The article is devoted to affine and wrap algebras over quaternions and octonions. Residues of functions of quaternion and octonion variables are studied. They are used for construction of such algebras. Their structure is investigated.
This article uses homological methods for evaluating compactly supported cohomology groups of noncompact toric surfaces
The purpose of this paper is to survey the structure of closed and transitive transformation groups acting on a closed surface. In particular, we prove a number of relations between groups acting on the sphere that contain the rotation…