Versal Deformations of a Dirac Type Differential Operator
نویسندگان
چکیده
منابع مشابه
Versal Deformations of a Dirac Type Differential Operator
If we are given a smooth differential operator in the variable x ∈ R/2πZ, its normal form, as is well known, is the simplest form obtainable by means of the Diff(S)-group action on the space of all such operators. A versal deformation of this operator is a normal form for some parametric infinitesimal family including the operator. Our study is devoted to analysis of versal deformations of a Di...
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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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We give more details about an integrable system [26] in which the Dirac operator D = d + d∗ on a graph G or manifold M is deformed using a Hamiltonian system D′ = [B, h(D)] with B = d − d∗ + βib. The deformed operator D(t) = d(t) + b(t) + d(t)∗ defines a new exterior derivative d(t) and a new Dirac operator C(t) = d(t) + d(t)∗ and Laplacian M(t) = C(t)2 and so a new distance on G or a new metri...
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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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ژورنال
عنوان ژورنال: Journal of Nonlinear Mathematical Physics
سال: 1999
ISSN: 1776-0852
DOI: 10.2991/jnmp.1999.6.3.1