Related papers: Deformations and elements of deformation theory
This is an introduction to the notion of local subgroupoid introduced by the author and R. Brown. It can also serve as an introduction to an application of sheaf theory, and so could be useful to beginners in that theory. The main results…
In the first section we recall some basic notions on Lie algebras. In a second time we study the algebraic variety of complex $n$-dimensional Lie algebras. We present different notions of deformations : Gerstenhaber deformations,…
We obtain a local stable manifold theorem for perturbations of nonautonomous linear difference equations possessing a very general type of nonuniform dichotomy, possibly with different growth rates in the uniform and nonuniform parts. We…
In this paper we study the Newton stratification on the reduction of Shimura varieties of PEL type with hyperspecial level structure and the Newton stratification on the deformation space of a Barsotti-Tate group with PEL structure. Our…
In this thesis we consider the geometry of the Hilbert scheme of points in P^n, concentrating on the locus of points corresponding to the Gorenstein subschemes of P^n. New results are given, most importantly we provide tools for…
We consider Voronoi's reduction theory of positive definite quadratic forms which is based on Delone subdivision. We extend it to forms and Delone subdivisions having a prescribed symmetry group. Even more general, the theory is developed…
We generalize the decomposition theorem for perverse sheaves to Artin stacks with affine stabilizers over finite fields.
This is the abstract prepared for Workshop on Topology and Geometry (Zhang jiang, China, October 1994), and is a review of my recent works. What kinds of combinations of singularities can appear in small deformation fibers of a fixed…
We consider anti-plane shear deformations of an incompressible elastic solid whose reference configuration is an infinite cylinder with a cross section that is unbounded in one direction. For a class of generalized neo-Hookean strain energy…
Assume a complete superstable theory is superstable, and let P be a class of regular types, typically closed under automorphisms of the monster and non-orthogonality. We define the notion of P-NDOP and prove the existence of…
We construct a Chern-Simons action for q-deformed gauge theory which is a simple and straightforward generalization of the usual one. Space-time continues to be an ordinary (commuting) manifold, while the gauge potentials and the field…
We give an explicit combinatorial description of the deformation theory of the Abelian category of (quasi)coherent sheaves on any separated Noetherian scheme $X$ via the deformation theory of path algebras of quivers with relations, by…
The construction and analysis of deformations of quantum field theories by warped convolutions is extended to a class of globally hyperbolic spacetimes. First, we show that any four-dimensional spacetime which admits two commuting and…
We use the Fock space representation of the quantum affine algebra of type $A^{(2)}_{2n}$ to obtain a description of the global crystal basis of its basic level 1 module. We formulate a conjecture relating this basis to decomposition…
We investigate the correspondence between three theories of deformations of rational surface singularities: de Jong and van Straten's picture deformations, Koll\'ar's P-resolutions, and Pinkham's smoothings of negative weights. We provide…
We determine the universal deformation over reduced base rings of the Witt ring scheme enhanced by a Frobenius lift and Verschiebung. It agrees with a q-deformation earlier introduced by the second author, for which we also give a simpler…
The paper is devoted to the study of homeomoephisms with finite distortion on the plane with use of the modulus techniques.
We give a conceptual explanation of universal deformation formulas for unital associative algebras and prove some results on the structure of their moduli spaces. We then generalize universal deformation formulas to other types of algebras…
This article provides a ``local'' complementary to the previous results concerning the local models for the moduli stacks of ``global'' $G$-shtukas. Here we study the geometry of Rapoport-Zink spaces for local $P$-shtukas by constructing…
Introducing the deformation theory of holomorphic Cartan geometries, we compute infinitesimal automorphisms and infinitesimal deformations. We also prove the existence of a semi-universal deformation of a holomorphic Cartan geometry.