Injective Analytic Maps - A Counterexample to the Proof

TL;DR

This paper identifies a critical flaw in a previous proof concerning the non-existence of certain injective analytic maps, providing a counterexample that challenges the original conjecture.

Contribution

It presents a counterexample that reveals an error in the earlier proof, questioning the validity of the conjecture about injective analytic maps.

Findings

Counterexample demonstrates the flaw in the original proof

Challenges the conjecture on the non-existence of specific injective maps

Reveals an unexpected property of a hypersurface germ in complex space

Abstract

In Duke Math. J. 69, No.2, 335-347 (1993) the author translates a conjecture of Le Dung Trang on the non-existence of injective analytic maps f:(C^n,0)->(C^{n+1},0) with df(0)=0 into the non-existence of a hypersurface germ in (C^{n+1},0) with rather unexpected properties. However, the proof given there contains an apparently fatal error, as we demonstrate with an example.