Related papers: Simple General Neron Desingularization in local ${…
After briefly recalling some computational aspects of blowing up and of representation of resolution data common to a wide range of desingularization algorithms (in the general case as well as in special cases like surfaces or binomial…
These lecture notes provide a unified overview of most known canonical desingularization methods in characteristic zero. It starts with discussing the classical method, and then proceeds with the recently discovered ones: logarithmic…
We prove that the algorithm for desingularization of algebraic varieties in characteristic zero of the first two authors is functorial with respect to regular morphisms. For this purpose, we show that, in characteristic zero, a regular…
We show that Ore operators can be desingularized by calculating a least common left multiple with a random operator of appropriate order. Our result generalizes a classical result about apparent singularities of linear differential…
In this note, we describe some desingularizations of some subvarieties of the cartesian powers of a semisimple Lie algebra of finite dimension.
A noncommutative algebra of the complex $q$-twistors and their differentials is considered on the basis of the quantum $GL_q (4)\times SL_q (2)$ group. Real and pseudoreal $q$-twistors are discussed too. We consider the quantum-group…
An approach to the Holographic Renormalization Group in the context of Rehren duality - a structural form of the AdS-CFT correspondence, in the context of Local Quantum Physics (Algebraic QFT) - is proposed. Special attention to the issue…
A simplicial set is said to be non-singular if the representing map of each non-degenerate simplex is degreewise injective. The inclusion into the category of simplicial sets, of the full subcategory whose objects are the non-singular…
A class of desingularizations for orbit closures of representations of Dynkin quivers is constructed, which can be viewed as a graded analogue of the Springer resolution. A stratification of the singular fibres is introduced; its geometry…
In this paper all deformations of the general linear group, subject to certain restrictions which in particular ensure a smooth passage to the Lie group limit, are obtained. Representations are given in terms of certains sets of creation…
A list of generic $U_q(sl_2)$-module algebra structures on the Laurent polynomial algebra over the quantum plane with uncountably many isomorphism classes is produced. Also, a complete list of such structures is presented in which the…
We construct a desingularization of the ``main component'' $\bar{\mathfrak M}_{1,k}^0(\Bbb{P}^n,d)$ of the moduli space $\bar{\mathfrak M}_{1,k}(\Bbb{P}^n,d)$ of genus-one stable maps into the complex projective space $\Bbb{P}^n$. As a…
A simple method is proposed for deforming $A_\infty$-algebras by means of the resolution technique. The method is then applied to the associative algebras of polynomial functions on quantum superspaces. Specifically, by introducing suitable…
We obtain a complete classification of minimal simple unitary $W$-algebras.
We study the partial resolutions of singularities related to Hilbert schemes of points on an affine space. Consider a quotient of a vector space $V$ by an action of a finite group $G$ of linear transforms. Under some additional assumptions,…
For any finitely generated abelian group $Q$, we reduce the problem of classification of $Q$-graded simple Lie algebras over an algebraically closed field of "good" characteristic to the problem of classification of gradings on simple Lie…
We define a new $q$-deformation of Brauer's centralizer algebra which contains Hecke algebras of type $A$ as unital subalgebras. We determine its generic structure as well as the structure of certain semisimple quotients. This is expected…
We identify families of commutative rings that can be written as a direct limit of a directed system of noetherian regular rings and investigate the homological properties of such rings.
We continue our study of minimal affinizations for algebras of type D, E.
The algebraic method of singular reduction is applied for non regular group action on manifolds which provides singular symplectic spaces. The problem of deformation quantization of the singular surfaces is the focus. For some examples of…