Kiumars
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Registered User
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Assistant Prof. at Univ. of Pittsburgh
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Apr 2 |
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Fubini-Study metric for an infinite dimensional Hilbert space Thanks Ahmed and Alvarez, so definition works as in the finite dimensional case. |
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Mar 30 |
asked | Fubini-Study metric for an infinite dimensional Hilbert space |
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Mar 25 |
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Initial ideal of k-th power of an ideal Sorry Youngsu for confusion. |
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Mar 25 |
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Initial ideal of k-th power of an ideal Here 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 ${\bf k}$. |
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Mar 25 |
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Initial ideal of k-th power of an ideal Youngsu: 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. |
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Mar 19 |
asked | Initial ideal of k-th power of an ideal |
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Feb 17 |
awarded | ● Yearling |
