Related papers: Deformations of Border Bases
Multiparameter persistent homology has emerged as a powerful generalization of topological data analysis, capable of encoding multivariate filtrations. However, the algebraic complexity of multiparameter persistence modules, marked by wild…
The aim of this paper is to review the deformation theory of $n$-Lie algebras. We summarize the 1-parameter formal deformation theory and provide a generalized approach using any unital commutative associative algebra as a deformation base.…
Geometric modeling by constraints, whose applications are of interest to communities from various fields such as mechanical engineering, computer aided design, symbolic computation or molecular chemistry, is now integrated into standard…
We present an overview of some recent developments in the theory of generalized formal series, grounded in diffeological geometric framework. These constructions aim to offer new tools for understanding infinite-dimensional phenomena in…
We consider the Rosenfeld-Groebner algorithm for computing a regular decomposition of a radical differential ideal generated by a set of ordinary differential polynomials in n indeterminates. For a set of ordinary differential polynomials…
We propose a geometric and categorical approach to the Hodge Conjecture for all smooth projective complex varieties. By embedding any such variety into a flat family with general fibers smooth complete intersections, we prove the conjecture…
The set of common roots of a finite set $I$ (it is an ideal) of homogeneous polynomials is known as projective algebraic set $V$. In this article I show how to dualize such projective algebraic sets $V$ by elimination of variables from a…
We study "straight equisingular deformations", a linear subfunctor of all equisingular deformations and describe their seminuniversal deformation by an ideal containing the fixed Tjurina ideal. Moreover, we show that the base space of the…
A new scheme is proposed for dealing with the problem of singularities in General Relativity. The proposal is, however, much more general than this. It can be used to deal with manifolds of any dimension which are endowed with nothing more…
Standard noncommutative Gr\"obner basis procedures are used for computing ideals of free noncommutative polynomial rings over fields. This paper describes Gr\"obner basis procedures for one-sided ideals in finitely presented noncommutative…
The theory of complete generalized Jordan sets is employed to reduce the PDE with the irreversible linear operator $B$ of finite index to the regular problems. It is demonstrated how the question of the choice of boundary conditions is…
In affine formation control problems, the construction of the framework with universal rigidity and affine localizability is a critical prerequisite, but it has not yet been well addressed, especially when additional agents join the…
It has been discovered that linear codes may be described by binomial ideals. This makes it possible to study linear codes by commutative algebra and algebraic geometry methods. In this paper, we give a decoding algorithm for binary linear…
We develop a general deformation principle for families of Riemannian metrics on smooth manifolds with possibly non-compact boundary, preserving lower scalar curvature bounds. The principle is used in order to strengthen boundary…
The increasing demand for Fourier transforms on geometric algebras has resulted in a large variety. Here we introduce one single straight forward definition of a general geometric Fourier transform covering most versions in the literature.…
The purpose of this paper is to present a new mathematical model for the deformation of thin Cosserat elastic plates. Our approach, which is based on a generalization of the classical Reissner plate theory, takes into account the transverse…
In his seminal Inventiones paper from 1972 Grauert proved the existence of a semiuniversal deformation of an arbitrary complex analytic isolated singularity. For the proof he invented an approximation theorem for solving a system of…
A contemporary and exciting application of Groebner bases is their use in computational biology, particularly in the reverse engineering of gene regulatory networks from experimental data. In this setting, the data are typically limited to…
In this paper, the tropical differential Gr\"obner basis is studied, which is a natural generalization of the tropical Gr\"obner basis to the recently introduced tropical differential algebra. Like the differential Gr\"obner basis, the…
Let $\Bbbk$ be an algebraically closed field and $\Lambda$ a generalized Brauer tree algebra over $\Bbbk$. We compute the universal deformation rings of the periodic string modules over $\Lambda$. Moreover, for a specific class of…