reduced fibers and openness - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-23T00:08:50Z http://mathoverflow.net/feeds/question/75494 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/75494/reduced-fibers-and-openness reduced fibers and openness kaddar 2011-09-15T07:45:53Z 2011-09-15T07:45:53Z <p>Hi, everybody.</p> <p>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?</p> <p>Rk: The result is true for flat morphism.</p> <p>Thank you.</p>