I need a version of the parametric transversality theorem for the complex case. The original one is:

Let $M,\ N,\ Z,\ S$ be smooth manifolds. If a smooth map $F\colon M\times S \rightarrow N\supset Z$ is transversal to $Z,$ then for almost all $s\in S,$ $F_s$ is transversal to $Z.$

I'd like a reference for the version of this statement for complex manifolds and a holomorphic map $F$.

  • 1
    $\begingroup$ I'm probably missing something, but doesn't the statement for the underlying smooth manifolds of the complex manifolds provide what you need? $\endgroup$ Nov 21 '17 at 16:27
  • $\begingroup$ I think so, but I never saw any version of it for the holomorphic maps and complex manifolds. I would like to see a reference just to be sure I'm not missing some important detail. $\endgroup$
    – clementine
    Nov 21 '17 at 16:33

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