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A Characteristic Property of Injective Holomorphic Germs

Authors:	Emmanuel Preissmann

Affiliation:	(1) Grenoble, France

Abstract:	Let X ₀ be the germ at 0 of a complex variety and let $f: X_0rightarrow {Bbb C}^n_0$ be a holomorphic germ. We say that f is pseudoimmersive if for any $g: {Bbb R}_0rightarrow X_0$ such that $f circ g in C^{infty}$ , we have $gin C^{infty}$ . We prove that f is pseudoimmersive if and only if it is injective. Some results about the real case are also considered.

Keywords:	2000 Mathematics Subject Classification: 58C27 57R42 32B15
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