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Zbl 0721.32003
Hauser, Herwig; Müller, Gerd
Analytic curves in power series rings. (English)
[J] Compos. Math. 76, No.1-2, 197-201 (1990). ISSN 0010-437X; ISSN 1570-5846/e

Let f: $S\to (V,v)$ be an analytic map, where S is a reduced analytic space and (V,v) is the germ at v of a finite-dimensional complex vector space V. Let G be an algebraic subgroup of GL(V). Then it is easy to see that the following statements hold: $(i)\quad the$ germ T of points t in S for which f(t)$\in Gv$, is analytic; and $(ii)\quad there$ is an analytic map germ g: $T\to (G,1)$ such that $f(t)=g(t)v$ for every $t\in T.$ \par The aim of the paper under review is to prove similar statements in the (far less obvious) case where $V={\cal O}\sp p\sb n$ (where ${\cal O}\sb n$ is the convergent power series ${\bbfC}$-algebra in n variables) and $G=GL\sb p({\cal O}\sb n)\rtimes Aut({\cal O}\sb n)$ is the contact group acting naturally on ${\cal O}\sp p\sb n$.
[L.Bădescu (Bucureşti)]

MSC 2000:: *32B10 Germs of analytic sets
14L30 Group actions on varieties or schemes
32B05 Analytic algebras and generalizations
13J07 Analytic algebras and rings
14L35 Classical groups (geometric aspects)

Keywords: orbits; analytic germs of singularities; group actions; convergent power series; contact group

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