Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

Hi. Can, every one, give me an example of finite surjective morphism of finite tor dimension (but not flat!) between reduced schemes or complex analytic spaces... Thank you.

share|improve this question

1 Answer 1

Consider a smooth surface $Y$ with a point $p\in Y$. Let $X$ be obtained by gluing two copies of $Y$ at $p$, with the obvious morphism $X \to Y$. This is surjective and finite, and has finite Tor-dimension (because $Y$ is regular, hence every morphism to $Y$ has finite Tor dimension). However, it is not flat (for example, because $X$ is not Cohen-Macaulay).

share|improve this answer
    
thank you very much Angelo. In fact, all flat and surjective morphims with no Cohen-Macaulay fibers gives, by finite projection or Noether quasi-normalization, finite tor dimension morphism... –  kaddar Jun 18 '10 at 7:17

Your Answer

 
discard

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.