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Versal deformations of formal arcs

Mikhail Grinberg·David Kazhdan
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Abstract

Let X be a complex algebraic variety, and L(X) be the scheme of formal arcs in X. Let f be an arc whose image is not contained in the singularities of X. We show that the formal neighborhood of f in L(X) admits a decomposition into a product of an infinite-dimensional smooth piece, and a piece isomorphic to the formal neighborhood of a closed point of a scheme of finite type.

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Mikhail Grinberg, David Kazhdan. 1998-12-17. Versal deformations of formal arcs. https://arxiv.org/abs/math/9812104

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