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Let $f:X\rightarrow Y$ be a flat morphism of schemes, with an irreducible locally Noetherian target. Call a condition on the fibers of $f$ "good" if the condition holds at the generic point of $Y$ iff it holds on a non-empty open set. What are some geometrically interesting examples of non-constructible "good" conditions on the fibers?

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  • $\begingroup$ What do you mean by constructible? $\endgroup$ Apr 13, 2019 at 16:44
  • $\begingroup$ @AviSteiner the locus where this condition holds is a constructible subset of the target. $\endgroup$
    – user137767
    Apr 13, 2019 at 16:50

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