Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Versal deformations of formal arcs   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.

37
The categories of this paper are: supr-con
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The categories of this paper are: cmp-lg
1
The categories of this paper are: cs
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The categories of this paper are: mtrl-th
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The categories of this paper are: ao-sci
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The categories of this paper are: funct-an
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The categories of this paper are: math-ph
9
The categories of this paper are: nlin
11
The categories of this paper are: hep-lat
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The categories of this paper are: acc-phys
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The categories of this paper are: solv-int
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The categories of this paper are: q-fin
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The categories of this paper are: bayes-an
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The categories of this paper are: chao-dyn
13
The categories of this paper are: quant-ph
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The categories of this paper are: patt-sol