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deleted 11 characters in body; edited title

edited Aug 28, 2020 at 15:55

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Non-uniruled connected smooth fibers implies flat

Let $f:X\to Y$ be a surjective morphism of connected smooth projective varieties over an algebraically closed field.

Assume all fibers are connected smooth and none are uniruled. Is $f$ flat?

ag.algebraic-geometry moduli-spaces birational-geometry

asked Aug 28, 2020 at 11:18

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