# reduced fibers and openness

Hi, everybody.

Is the following true: If $f:X\rightarrow S$ is an open (or universally open in A.G) morphism of complex spaces with pure dimensional reduced fibers over reduced base $S$. Is $X$ reduced?

Rk: The result is true for flat morphism.

Thank you.

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This question is very similar to your earlier questions mathoverflow.net/questions/51004/flat-map-with-reduced-fibers, and mathoverflow.net/questions/51373/… Are you sure you can't figure it out from these answers? –  J.C. Ottem Sep 15 '11 at 9:11
Dear J.C. Here, we assume the morphism only to be open and not flat. And then flatness give us that $X$ is generically reduced and perhaps not reduced at all ! –  kaddar Sep 15 '11 at 9:27