Analytic varieties versus integral varieties of Lie algebras of vector fields

Authors:
Herwig Hauser and Gerd Müller

Journal:
Bull. Amer. Math. Soc. **26** (1992), 276-279

MSC (2000):
Primary 32B10; Secondary 17B40

MathSciNet review:
1121570

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Abstract: We associate to any germ of an analytic variety a Lie algebra of tangent vector fields, the *tangent algebra*. Conversely, to any Lie algebra of vector fields an analytic germ can be associated, the *integral variety*. The paper investigates properties of this correspondence: The set of all tangent algebras is characterized in purely Lie algebra theoretic terms. And it is shown that the tangent algebra determines the analytic type of the variety.

**[HM1]**H. Hauser and G. Müller,*Analytic varieties and Lie algebras of vector fields*. Part I:*The Gröbner correspondence*, preprint 1991. To be published.**[HM2]**-,*Analytic varieties and Lie algebras of vector fields*. Part II:*Singularities are determined by their tangent algebra*(to appear).**[N]**Raghavan Narasimhan,*Analysis on real and complex manifolds*, Advanced Studies in Pure Mathematics, Vol. 1, Masson & Cie, Éditeurs, Paris; North-Holland Publishing Co., Amsterdam, 1968. MR**0251745****[O]**Hideki Omori,*A method of classifying expansive singularities*, J. Differential Geom.**15**(1980), no. 4, 493–512 (1981). MR**628340****[R]**Hugo Rossi,*Vector fields on analytic spaces*, Ann. of Math. (2)**78**(1963), 455–467. MR**0162973**

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DOI:
http://dx.doi.org/10.1090/S0273-0979-1992-00272-0

Article copyright:
© Copyright 1992
American Mathematical Society