Let $C, X$ be a smooth projective variety over an algebraically closed field. Suppose $f:X \to C$ is a flat, proper morphism with geometrically irreducible fibers. Is the relative tangent space $\mathcal{T}_f$, associated to this morphism, flat as an $\mathcal{O}_X$-module?
2026-03-26 18:58:44.1774551524
Relative tangent space and flatness
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