Related papers: Algebraic Shifting and f-Vector Theory
The theory of modular deformations is generalized for the category of complex analytic polyhedra which includes germs of complex space as well as any compact complex analytic space. The objective of the theory is a construction of fine…
We study a tentative generally covariant quantum field theory, denoted the T-Theory, as a tool to investigate the consistency of quantum general relativity. The theory describes the gravitational field and a minimally coupled scalar field;…
The set of f-vectors of pure simplicial complexes is an important but little understood object in combinatorics and combinatorial commutative algebra. Unfortunately, its explicit characterization appears to be a virtually intractable…
Let $V$ be a vertex operator algebra and $g$ an automorphism of finite order. We construct an associative algebra $A_g(V)$ and a pair of functors between the category of $A_g(V)$-modules and a certain category of admissible $g$-twisted…
This is an expository paper which gives a simple arithmetic introduction to the conjectures of Weil and Dwork concerning zeta functions of algebraic varieties over finite fields. A number of further open questions are raised.
This article has the following aims: (1) Extend the notion of fuchsian singularities (of first kind) to base fields of arbitrary characteristic. (2) Discuss their relationship to mathematical objects of a different nature. (3) Provide a…
In this paper, we study the well-know $g$-conjecture for rational homology spheres in a topological way. To do this, we construct a class of topological spaces with torus actions, which can be viewed as topological generalizations of toric…
This expository paper starts with a brief survey on the relation between partitions and surjections of sets, and then gives a quick introduction to the theories of incidence algebras, Segal groupoids and combinatorial species. The aim is to…
The main purpose of this paper is to lay the foundations of a general theory which encompasses the features of the classical Hough transform and extend them to general algebraic objects such as affine schemes. The main motivation comes from…
First and second fundamental theorems are given for polynomial invariants of a class of pseudo-reflection groups (including the Weyl groups of type $B_n$), under the assumption that the order of the group is invertible in the base field.…
In analogy to valued fields, we study model-theoretic properties of valued vector spaces with variable base field by proving transfer principles down to the skeleton and down to the value set and base field. For instance, we give a formula…
This article investigates the homotopy theory of simplicial commutative algebras with a view to homological applications.
We generalize the celebrated Fr\"{o}berg's theorem to embedded joins of copies of a simplicial complex, namely higher secant complexes to the simplicial complex, in terms of property $N_{q+1,p}$ due to Green and Lazarsfeld. Furthermore, we…
We consider the algebra of Hecke correspondences (elementary transformations at a single point) acting on the algebraic K-theory groups of the moduli spaces of stable sheaves on a smooth projective surface S. We derive quadratic relations…
This text is a survey of derived algebraic geometry. It covers a variety of general notions and results from the subject with a view on the recent developments at the interface with deformation quantization.
It is well-known that the theories of semi-vector spaces and semi-algebras -- which were not much studied over time -- are utilized/applied in Fuzzy Set Theory in order to obtain extensions of the concept of fuzzy numbers as well as to…
One of the most common and effective methods of obtaining structural information on simplicial complexes is to use tools from algebraic geometry/commutative algebra (often motivated by properties of toric varieties). However, there is no…
Given an infinite field $\mathbb{k}$ and a simplicial complex $\Delta$, a common theme in studying the $f$- and $h$-vectors of $\Delta$ has been the consideration of the Hilbert series of the Stanley--Reisner ring $\mathbb{k}[\Delta]$…
In this brief review, we present the results of the fractional differential approach in cosmology in the context of the exact models of cosmological accelerated expansion obtained by several authors to date. Most of these studies are…
Theory of representations of F-algebra is a natural development of the theory of F-algebra. Exploring of morphisms of the representation leads to the concepts of generating set and basis of representation. In the book I considered the…