Suppose $f: X \to Y$ is a surjective, flat morphism of varieties over an algebraically closed field $k$ of characteristic zero. Suppose $X$ is smooth over $k$ and $Y$ is integral with fraction field $K_Y$. Is the generic fiber $X_{gen}$ automatically smooth over $K_Y$?
2026-03-25 12:27:11.1774441631
Smoothness of general fiber of flat morphism
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