Deformations of Lie algebras of vector fields arising from families of schemes

Details Deformations of Lie algebras of vector fields arising from families of schemes Deformations of Lie algebras of vector fields arising from families of schemes

2007-07-27

arxiv.org/abs/0707.4054v1

Mathematics

Algebraic Geometry

20 pages

Scientific paper

10.1016/j.geomphys.2007.10.003

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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