Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Deformations of Lie algebras of vector fields arising from families of
  schemes   Fialowski and Schlichenmaier constructed examples of global deformations of
Lie algebras of vector fields from deforming the underlying variety. We
formulate their approach in a conceptual way. Namely, we construct a stack of
deformations and a morphism form the moduli stack of stable marked curves. The
morphism associates to a family of marked curves the family of Lie algebras
obtained by taking the Lie algebra of vertical vector fields on the family
where one has extracted the marked points. We show that this morphism is almost
a monomorphism by Pursell-Shanks theory.

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The categories of this paper are: atom-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: funct-an
3
The categories of this paper are: physics
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The categories of this paper are: solv-int
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The categories of this paper are: eess
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The categories of this paper are: nlin
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-th
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The categories of this paper are: q-bio
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The categories of this paper are: supr-con
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The categories of this paper are: nucl-ex
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The categories of this paper are: quant-ph