共查询到20条相似文献,搜索用时 46 毫秒
1.
Laurent Meersseman 《Comptes Rendus Mathematique》2014,352(2):143-145
In this note, we propose a definition of local moduli space in a general framework including the case of CR structures on a fixed differentiable manifold. We show that it is the same as the notion of versal deformation space for complex structures. Finally, we test this definition on the spaces constructed in [5] and [6]. 相似文献
2.
In this paper we study which solutions to an embedding problem can be constructed using a versal deformation of a group representation
over an algebraically closed field of positive characteristic. This question reduces (at least stably) to finding which representations
of finite groups have faithful versal deformations. We determine exactly when a versal deformation of a representation of
a finite group is faithful in case the representation belongs to a cyclic block and its endomorphisms are given by scalar
multiplications.
Received: January 30, 2001 相似文献
3.
4.
We introduce the notion of microlocal versal deformation of a plane curve. We construct equisingular versal deformations of Legendrian curves that are the conormal of a semi-quasi-homogeneous branch. To cite this article: J. Cabral, O. Neto, C. R. Acad. Sci. Paris, Ser. I 347 (2009). 相似文献
5.
We discuss the notion of singular formal deformation in algebraic setup. Such deformations show up in both finite and infinite dimensional structures. It turns out that there is a stronger version of singular deformation—called essentially singular—which arises from a singular curve in the base of the versal deformation. 相似文献
6.
Laurent Stolovitch 《Numerical Algorithms》1993,4(1):25-46
The aim of this article is to present algorithms for the computation of versal deformations of matrices. A deformation of a matrixA
0 is a holomorphic matrix-valued function whose value at a pointt
0C
p
is the matrixA
0. We want to study the properties of these matrices in a neighbourhood oft
0. One could, for each valuet in this neighbourhood, compute the Jordan form as well as the change of basis matrix; but, generally, the results will not be analytic. So, we want to construct a deformation of the matrixA
0 into which any deformation can be transformed by an invertible deformation of the matrixId. After having introduced the notion of versal deformation, we shall provide computer algebra algorithms to computer these normal forms. In the last section, we shall show that a one-parameter deformation can be transformed into a simpler form than the general versal deformation. 相似文献
7.
Nathan Owen Ilten 《Journal of Pure and Applied Algebra》2009,213(6):1086-1096
In the case of two-dimensional cyclic quotient singularities, we classify all one-parameter toric deformations in terms of certain Minkowski decompositions introduced by Altmann [Minkowski sums and homogeneous deformations of toric varieties, Tohoku Math. J. (2) 47 (2) (1995) 151-184.]. In particular, we show how to induce each deformation from a versal family, describe exactly to which reduced versal base space components each such deformation maps, describe the singularities in the general fibers, and construct the corresponding partial simultaneous resolutions. 相似文献
8.
In this paper we study formal moduli for wildly ramified Galois covering. We prove a local-global principle. We then focus
on the infinitesimal deformations of the Z/p
Z-covers. We explicitly compute a deformation of an automorphism of order p which implies a universal obstruction for p>2. By deforming Artin-Schreier equations we obtain a lower bound on the dimension of the local versal deformation ring. At
last, by comparing the global versal deformation ring to the complete local ring in a point of a moduli space, we determine
the dimensions of the global and local versal deformation rings.
Oblatum 22-II-1999 & 15-XII-1999?Published online: 29 March 2000 相似文献
Déformations formelles des revêtements sauvagement ramifiés de courbes algébriques
Oblatum 22-II-1999 & 15-XII-1999?Published online: 29 March 2000 相似文献
9.
Pietro-Luciano Buono 《Journal of Differential Equations》2003,193(2):307-342
We consider parametrized families of linear retarded functional differential equations (RFDEs) projected onto finite-dimensional invariant manifolds, and address the question of versality of the resulting parametrized family of linear ordinary differential equations. A sufficient criterion for versality is given in terms of readily computable quantities. In the case where the unfolding is not versal, we show how to construct a perturbation of the original linear RFDE (in terms of delay differential operators) whose finite-dimensional projection generates a versal unfolding. We illustrate the theory with several examples, and comment on the applicability of these results to bifurcation analyses of nonlinear RFDEs. 相似文献
10.
O. V. Lyashko 《Journal of Mathematical Sciences》1984,27(3):2736-2759
The geometry of a bifurcation diagram in the base of a versal deformation of a singularity is studied for single singularities on a manifold with boundary. In particular, vector fields and groups of diffeomorphisms are studied which are defined in a neighborhood of a bifurcation diagram as are stratification of a bifurcation diagram and decomposition of singularities.Translated from Itogi Nauki i Tekhniki, Seriya Sovremennye Problemy Matematiki, Vol. 22, pp. 94–129, 1983. 相似文献
11.
Wendy Lowen 《Advances in Mathematics》2005,198(1):172-221
This paper continues the development of the deformation theory of abelian categories introduced in a previous paper by the authors. We show first that the deformation theory of abelian categories is controlled by an obstruction theory in terms of a suitable notion of Hochschild cohomology for abelian categories. We then show that this Hochschild cohomology coincides with the one defined by Gerstenhaber, Schack and Swan in the case of module categories over diagrams and schemes and also with the Hochschild cohomology for exact categories introduced recently by Keller. In addition we show in complete generality that Hochschild cohomology satisfies a Mayer-Vietoris property and that for constantly ringed spaces it coincides with the cohomology of the structure sheaf. 相似文献
12.
Mauricio D Garay 《Topology》2004,43(5):1081-1088
We introduce a cohomological approach to isochore deformation problems. We use this formulation in order to prove an isochore versal deformation theorem for holomorphic function germs. 相似文献
13.
Wendy Lowen Michel Van den Bergh 《Transactions of the American Mathematical Society》2006,358(12):5441-5483
In this paper we develop the basic infinitesimal deformation theory of abelian categories. This theory yields a natural generalization of the well-known deformation theory of algebras developed by Gerstenhaber. As part of our deformation theory we define a notion of flatness for abelian categories. We show that various basic properties are preserved under flat deformations, and we construct several equivalences between deformation problems.
14.
For the unfolding of equivariant bifurcation problems with two types of state variables in the presence of parameter symmetry,the versal unfolding theorem with respect to left-right equivalence is obtained by using the related methods and techniques in the singularity theory of smooth map-germs.The corresponding results in[4,9]can be considered as its special cases.A relationship between the versal unfolding w.r.t.left-right equivalence and the versal deformation w.r.t.contact equivalence is established. 相似文献
15.
Javier Fernández de Bobadilla 《Topology》2004,43(4):925-982
In this paper we develop a Morsification Theory for holomorphic functions defining a singularity of finite codimension with respect to an ideal, which recovers most previously known morsification results for non-isolated singularities and generalise them to a much wider context. We also show that deforming functions of finite codimension with respect to an ideal within the same ideal respects the Milnor fibration. Furthermore we present some applications of the theory: we introduce new numerical invariants for non-isolated singularities, which explain various aspects of the deformation of functions within an ideal; we define generalisations of the bifurcation variety in the versal unfolding of isolated singularities; applications of the theory to the topological study of the Milnor fibration of non-isolated singularities are presented. Using intersection theory in a generalised jet-space we show how to interpret the newly defined invariants as certain intersection multiplicities; finally, we characterise which invariants can be interpreted as intersection multiplicities in the above mentioned generalised jet space. 相似文献
16.
M. D. Garay 《Proceedings of the Steklov Institute of Mathematics》2007,259(2):35-59
We study deformation theory for quantum integrable systems and prove several theorems concerning the Gevrey convergence and
the unicity of perturbative expansions.
à V.I. Arnold pour ses 70 ans 相似文献
17.
Olav Arnfinn Laudal 《Acta Appl Math》2008,101(1-3):191-204
In the papers (Laudal in Contemporary Mathematics, vol. 391, [2005]; Geometry of time-spaces, Report No. 03, [2006/2007]), we introduced the notion of (non-commutative) phase algebras (spaces) Ph
n
(A), n=0,1,…,∞ associated to any associative algebra A (space), defined over a field k. The purpose of this paper is to study this construction in some more detail. This seems to give us a possible framework
for the study of non-commutative partial differential equations. We refer to the paper (Laudal in Phase spaces and deformation
theory, Report No. 09, [2006/2007]), for the applications to non-commutative deformation theory, Massey products and for the construction of the versal family
of families of modules. See also (Laudal in Homology, Homotopy, Appl. 4:357–396, [2002]; Proceedings of NATO Advanced Research Workshop, Computational Commutative and Non-Commutative Algebraic Geometry, [2004]).
相似文献
18.
The notion of Higgs-de Rham flows was introduced by Lan et al.(2019), as an analogue of YangMills-Higgs flows in the complex nonabelian Hodge theory. In this paper we investigate a small part of this theory, and study those Higgs-de Rham flows which are of level zero. We improve the original definition of level-zero Higgs-de Rham flows(which works for general levels), and establish a Hitchin-Simpson type correspondence between such objects and certain representations of fundamental groups in positive characteristic,which generalizes a classical results of Katz(1973). We compare the deformation theories of two sides in the correspondence, and translate the Galois action on the geometric fundamental groups of algebraic varieties defined over finite fields into the Higgs side. 相似文献
19.
Jan Arthur Christophersen 《Advances in Mathematics》2011,(2):801
The versal deformation of Stanley–Reisner schemes associated to equivelar triangulations of the torus is studied. The deformation space is defined by binomials and there is a toric smoothing component which I describe in terms of cones and lattices. Connections to moduli of abelian surfaces are considered. The case of the Möbius torus is especially nice and leads to a projective Calabi–Yau 3-fold with Euler number 6. 相似文献
20.
Systems of quasilinear first order PDE are studied in the framework of contact manifold. All of the local stable geometric
solutions of such systems are classified by using versal deformation and the classification of stable map germs of type Σ1 in singularity theory. 相似文献