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# properties of the fibers of a flat morphism

Let $X$ be an arbitrary scheme of finite type over $\mathbb{C}$ and $f:X \rightarrow \mathbb{A}_{\mathbb{C}}^1$ be a flat morphism. I suppose that the special fiber have some nice property, I would like to know if in that case the generic fiber has the same property. More precisely, I have in mind one of the following things:

1) the special fiber is reduced;

2) the special fiber is irreducible, but not necessarly reduced;

3) the special fiber is normal/smooth.

Thank you by adance for your answers or your references (there is things like that in the book of Matsumura but not these precise things).