# Is this morphism flat?

Suppose $X$ is a smooth projective curve over an algebraically closed field $k$.

Is the morphism $X \to \operatorname{Spec}(k)$ necessarily flat?

What kind of conditions on the above morphism are equivalent to the hypothesis of $X$ being smooth and projective?

• To answer your second question, $X$ is smooth and projective iff the morphism is smooth and projective. I'm not sure what else you could expect. – user64687 Feb 3 '14 at 14:02