I am asking for a *reference* for the following lemma (for which I know a proof). > **Lemma.** Let $f\colon X\to Y$ be a surjective morphism of irreducible ***smooth*** complex algebraic varieties (separated, reduced, irreducible schemes of finite type over $\Bbb C$) with ***smooth*** fibres of the same dimension $\dim X-\dim Y$ over closed points of $Y$. Then the morphism $f$ is smooth. Feel free to migrate this elementary question to Mathematics StackExchange.