Transformation to versal deformations of matrices
نویسندگان
چکیده
منابع مشابه
Approximation of Versal Deformations
In Artin’s work on algebraic spaces and algebraic stacks [A2], [A3], a crucial ingredient is the use of his approximation theorem to prove the algebraizability of formal deformations under quite general conditions. The algebraizability result is given in [A2, Thm 1.6], and we recall the statement now (using standard terminology to be recalled later). Theorem 1.1. (Artin) Let S be a scheme local...
متن کاملComputing Versal Deformations
Introduction 1. How to Solve the Deformation Equation 2. Deformations of Singularities 3. Smoothing Components of Curves 4. The Versal Deformation of L14 5. Remarks References Acknowledgement Electronic Availability In recent years I have computed versal deformations of various singularities, partly by hand, but mostly with the program Macaulay. I explain here how to do these computations. As a...
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Let X be a complex algebraic variety, and X◦ ⊂ X be the smooth part of X. Consider the scheme L(X) of formal arcs in X. The C-points of L(X) are just maps D = SpecC[[t]] → X (see, for example, [DL] for a definition of L(X) as a scheme). Let L◦(X) be the open subscheme of arcs whose image is not contained in X \X◦. Fix an arc γ : D → X in L◦(X), and let L(X)γ be the formal neighborhood of γ in L...
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We study the set M of pairs (f, V ), defined by an endomorphism f of F and a ddimensional f–invariant subspace V . It is shown that this set is a smooth manifold that defines a vector bundle on the Grassmann manifold. We apply this study to derive conditions for the Lipschitz stability of invariant subspaces and determine versal deformations of the elements of M with respect to a natural equiva...
متن کاملA Geometric Approach to Perturbation Theory of Matrices and Matrix Pencils. Part I: Versal Deformations∗
We derive versal deformations of the Kronecker canonical form by deriving the tangent space and orthogonal bases for the normal space to the orbits of strictly equivalent matrix pencils. These deformations reveal the local perturbation theory of matrix pencils related to the Kronecker canonical form. We also obtain a new singular value bound for the distance to the orbits of less generic pencil...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2001
ISSN: 0024-3795
DOI: 10.1016/s0024-3795(01)00346-9