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Note on convergence and orders of vanishing along curves. (English) Zbl 0711.32002

Let X be a complex space and C a family of curves passing through a point x in X. Using a theorem due to Gabrielov, the author gives conditions under which a formal function germ at x is convergent (or, respectively, has a high order of vanishing) when this property holds along all the curves in the family C.
Reviewer: A.Dimca

MSC:

32A05 Power series, series of functions of several complex variables
32B05 Analytic algebras and generalizations, preparation theorems
13J05 Power series rings
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References:

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