MathOverflow will be down for maintenance for approximately 3 hours, starting Monday evening (06/24/2013) at approximately 9:00 PM Eastern time (UTC-4).

Kiumars

 301 Reputation 169 views

Registered User

 Name Kiumars Member for 1 year Seen May 1 at 15:27 Website Location Pittsburgh Age 38
Assistant Prof. at Univ. of Pittsburgh
 Apr2 comment Fubini-Study metric for an infinite dimensional Hilbert spaceThanks Ahmed and Alvarez, so definition works as in the finite dimensional case. Mar30 asked Fubini-Study metric for an infinite dimensional Hilbert space Mar25 comment Initial ideal of k-th power of an idealSorry Youngsu for confusion. Mar25 comment Initial ideal of k-th power of an idealHere by "primary" I mean m-primary where $\mathfrak{m}$ is the maximal ideal generated by $x_1, \ldots, x_n$. Nevertheless if $\mathfrak{n}$ is another maximal ideal and $I$ is $\mathfrak{n}$-primary then $S/I$ is finite dimensional over ${\bf k}$. Mar25 comment Initial ideal of k-th power of an idealYoungsu: It follows from the following observations: $I$ is primary iff $S/I$ is finite dimensional as a vector space over $k$. Since $\dim(S/I) = \dim(S/ in(I))$ it follows that $in(I)$ is also primary. Now for any $k > 0$, $in(I)^k$ should be primary. Thus $S/in(I)^k$ is finite dimensional which implies that $in(I^k) / in(I)^k$ is also finite dimensional. Mar19 asked Initial ideal of k-th power of an ideal Feb17 awarded ● Yearling