6
$\begingroup$

Let $A$ be an integral complete local ring over a field which is complete intersection.

Let $B$ be a normalization of $A$.

Q. Is $B$ Gorenstein?

I guess that even the normalization of Gorenstein local ring should be Gorenstein.

$\endgroup$
4
10
$\begingroup$

Consider $A=k[[x^3,x^2y,y^3]]\subset k[[x^3, x^2y, xy^2, y^3]]=B$. $B$ is the integral closure of $A$, $A$ is a hypersurface, but $B$ is not Gorenstein.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

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