Abstract
In this note, we provide the corrections to an article by D. Zaitsev, Acta Math., 183 (1999), 273-305. Building on a remark by S. Damour, we provide twenty counterexamples to the preprint version of the mentioned reference. Our main purpose is to establish shortly the algebraicity of a holomorphic mapping between real algebraic CR manifolds under a double reflection condition which generalizes the classical single reflection. A complete study of various double reflection conditions is also provided
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