Consider a morphism $$ f\colon X\to Y $$ between normal varieties. Let's say over the complex numbers. The geometric fibers of $f$ are irreducible.

I would like a criterion to detect the normality of the image of $f$. Maybe in term of the differential of $f$.

Thanks

Consider a projective flat morphism $$ f\colon X\to Y $$ between normal varieties. Let's say over the complex numbers. The geometric fibers of $f$ are all irreducible.

I would like a criterion to detect the normality (or the non-normality) of the image of $f$. Maybe in term of the differential of $f$.

Thanks