Related papers: Freeness for multiarrangements of hyperplanes over…
In a previous paper, we provided some update in the treatment of the finiteness theorem for rational maps of finite degree from a fixed variety to varieties of general type. In the present paper we present another improvement, introducing…
A general type of ray class fields of global function fields is investigated. The systematic computation of their genera leads to new examples of curves over finite fields with comparatively many rational points.
We compute the periods associated with a special class of hyperplane arrangements. In particular, we exhibit a combinatorial condition on the intersection lattice of a hyperplane arrangement that ensures that its associated periods are…
We consider skew free extensions of rings, also known as free multivariate skew polynomial rings, and explore some of the algebraic aspects of this construction. We give different characterizations of such rings and present conditions for…
We study maximal subalgebras of an arbitrary finite dimensional algebra over a field, and obtain full classification/description results of such algebras. This is done by first obtaining a complete classification in the semisimple case, and…
We present a Lagrangian approach to counting degrees of freedom in first-order field theories. The emphasis is on the systematic attainment of a complete set of constraints. In particular, we provide the first comprehensive procedure to…
We provide a clarification of the classification of two-dimensional algebras over an arbitrary base field. Using this clarification, we determine the number of non-isomorphic two-dimensional algebras over a finite field.
The review studies connections between integrable many-body systems and gauge theories. It is shown how the degrees of freedom in integrable systems are related with topological degrees of freedom in gauge theories. The relations between…
This article deals with the multiple values and algebraic dependences problem of meromorphic mappings sharing moving hyperplanes in projective space. We give some algebraic dependences theorems for meromorphic mappings sharing moving…
Hyperplane arrangements form the latest addition to the zoo of combinatorial objects dealt with by polymake. We report on their implementation and on a algorithm to compute the associated cell decomposition. The implemented algorithm…
This paper is devoted to the investigation of the property of order separability for HNN extensions and free products with commutative subgroups. Particularly it was proven that HNN extension of a free group with maximal connected cyclic…
We give a generalization of Gelfand's criterion on the commutativity of Hecke algebras for Gelfand pairs and multiplicity-free triples over algebraically closed fields of arbitrary characteristic. Using more lenient versions of projectivity…
In this paper we discuss various philosophical aspects of the hyperstructure concept extending networks and higher categories. By this discussion we hope to pave the way for applications and further developments of the mathematical theory…
Based on the notion of vectors and linear subspaces for a matroid, we develop a theory of flats and hyperplane arrangements for T-matroids, where T is a tract. This leads to several cryptomorphic descriptions of T-matroids: in terms of its…
In this paper we discuss the relationship between the moving planes of a rational parametric surface and the singular points on it. Firstly, the intersection multiplicity of several planar curves is introduced. Then we derive an equivalent…
The equations for topological fields in the $4d$ higher spin theory are considered. It is shown that these fields contain a finite number of degrees of freedom that justifies their naming. The issue of construction of gauge invariant…
We survey recent results on multiple transitivity of automorphism groups of affine algebraic varieties. We consider the property of infinite transitivity of the special automorphism group, which is equivalent to flexibility of the…
In 1989, Ziegler introduced the concept of a multi-arrangement. One natural example is the reflection arrangement of a unitary reflection group with multiplicity given by the number of reflections associated with each hyperplane. For all…
Broadly speaking, a finiteness property of groups is any generalisation of the property of having finite order. A large part of infinite group theory is concerned with finiteness properties and the relationships between them. Profinite…
It was proved that for any finite set of elements of a free product of residually finite groups such that no two of them belong to conjugate cyclic subgroups and each of them do not belong to a subgroup which is conjugate a to free factor…