Related papers: Notes on formal deformations of abelian categories
In a stable abelian group, we characterize generic types of cosets of type-definable subgroups.
This is the first paper in a series that studies smooth relative Lie algebra homologies and cohomologies based on the theory of formal manifolds and formal Lie groups. In this paper, we lay the foundations for this study by introducing the…
A general deformation theory of algebras which factorise into two subalgebras is studied. It is shown that the classification of deformations is related to the cohomology of a certain double complex reminiscent of the Gerstenhaber-Schack…
We will introduce formal frames of manifolds, which are a generalization of ordinary frames. Their fundamental properties are discussed. In particular, canonical forms are introduced, and torsions are defined in terms of them as a…
These notes briefly discuss basic notions concerning locally compact abelian topological groups and Fourier transforms of functions on them.
A notion of Hochschild cohomology of an abelian category was defined by Lowen and Van den Bergh (2005) and they showed the existence of a characteristic morphism from the Hochschild cohomology into the graded centre of the (bounded) derived…
In this paper we give a description of the first order deformation space of a regular embedding of reduced algebraic schemes. We compare our result with results of Ran (in particular [Ran, Prop. 1.3]).
We investigate deformations of functions on affine space, deformations in which the changes specialize to a distinguished point in the zero-locus of the original function. Such deformations enable us to obtain nice results on the cohomology…
After introducing some motivations for this survey, we describe a formalism to parametrize a wide class of algebraic structures occurring naturally in various problems of topology, geometry and mathematical physics. This allows us to define…
By analytic deformations of complex structures, we mean perturbations of the Dolbeault operator. By algebraic deformations of complex structures, we mean deformations of holomorphic glueing data. For complex manifolds there is,…
We introduce a notion of oriented dialgebra and develop a cohomology theory for oriented dialgebras based on the possibility to mix the standard chain complexes computing group cohomology and associative dialgebra cohomology. We also…
In this paper, we use (bi)semicosimplicial language to study the classical problem of infinitesimal deformations of a closed subscheme in a fixed smooth variety, defined over an algebraically closed field of characteristic 0. In particular,…
The content of this preprint together with additional material appears now in 0706.2154.
This is a survey on recent progress in algebraic deformation theory and the application of algebraic operads to its study. We review the classical homotopical tools in the theory of algebraic operads, namely Koszul duality. We give concrete…
This document aims to give a self-contained account of the parts of abelian group theory that are most relevant for algebraic topology. It is almost purely expository, although there are some slightly unusual features in the treatment of…
We present a method for generating new deformed solutions starting from systems of two real scalar fields for which defect solutions and orbits are known. The procedure generalizes the approach introduced in a previous work [Phys. Rev. D…
A complete description of the deformation classes of real ruled manifolds is given. In particular, we prove that once the complex deformation class is fixed, the real deformation class is prescribed by the topology of the real structure.
In this paper, we prove the smoothness of the functors of locally trivial deformations, flat deformations and log smooth deformations for irreducible type II degeneration of complex abelian surfaces.
We develop the notion of deformations using a valuation ring as ring of coefficients. This permits to consider in particular the classical Gerstenhaber deformations of associative or Lie algebras as infinitesimal deformations and to solve…
We describe the construction of the slice fibration of a given one.