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Let $M$ be a real analytic variety (if someone is concerned about distinction between "real analytic spaces" and "real analytic varieties" in real analytic geometry, let's assume that $M$ is both "...

Similarly to Morse lemma, a holomorphic Morse function can be written, near a critical point, as $W_1^2+W_2^2+...+W_n^2+C$ , for well chosen coordinates $W_1,W_2,...,W_n$. I want to cite this result ...