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...
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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 کاملEquivariant Versal Deformations of Semistable Curves
We prove that given any n-pointed prestable curve C of genus g with linearly reductive automorphism group Aut(C), there exists an Aut(C)equivariant miniversal deformation of C over an affine variety W . In other words, we prove that the algebraic stack Mg,n parametrizing n-pointed prestable curves of genus g has an étale neighborhood of [C] isomorphic to the quotient stack [W/Aut(C)].
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2002
ISSN: 0021-8693
DOI: 10.1016/s0021-8693(02)00144-8