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Apr 30, 2015 at 17:37 comment added abx An integer-valued function which is upper semi-continuous attains its minimum on an open subset.
Apr 30, 2015 at 17:34 comment added Higgs-Boson Thanks for your answer. Grauert's semi-continuity theorem states that $h^0(\mathcal{F}|_{X_y})$ is semi-continuous. How could we find the Zariski open set $U$ of $Y$ such that $h^0(\mathcal{F}|_{X_y})$ is constant in $U$?
Apr 30, 2015 at 17:13 history answered abx CC BY-SA 3.0