Sign up ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

Let $f: X\to Y$ be a finite (surjective) morphism between two algebraic varieties. I know when $X$ and $Y$ are non-singular and $\dim Y =1$, $f$ is flat. But in general, is it true that $f$ is a flat morphism?

share|cite|improve this question
See this question also:… –  Hailong Dao Apr 9 '10 at 2:45

1 Answer 1

up vote 6 down vote accepted

If X and Y are both regular, then this is true. In fact, it's true more generally if Y is regular and X is Cohen-Macaulay (Eisenbud, Commutative Algebra, Corollary 18.17). In general it's certainly false.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.