5
$\begingroup$

Suppose $R$ is a localization of a normal closed point of a variety of dimension $n$ over an algebraically closed field $k$ with maximal ideal $\mathfrak{m}$. Suppose also that the associated graded $\operatorname{Gr}_{\mathfrak{m}} R$ is isomorphic to the degree $d$ Veronese subring $S_d$ of $k[X_1,\ldots,X_n]$. Is this enough to conclude that the completion of $R$ is isomorphic to the completed local ring of $S_d$ at the origin? Are there counterexamples?

$\endgroup$

Your Answer

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

Browse other questions tagged or ask your own question.