## Cohen Macaulay locus in the relative setting

Hi.

I want to submit the following question:

Let $f:X\rightarrow S$ be a proper, surjective and open morphism of pure dimensional reduced complex spaces. Is it true that the Cohen Macaulay locus (point on which the fiber are C.M) of $f$ is dense in the fiber (i.e intersect the fibers in dense subset of the fiber) ?

Remark: It is true for $f$ flat by Banica result. Furthermore, if $f$ is flat and of type $S_{1}$ (i.e without embedded component in the fibers) this locus is of codimension >1 in the fibers.

Thank you.

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