162 reputation
18
bio website pitt.edu/~kaveh
location Pittsburgh
age 39
visits member for 2 years, 2 months
seen Apr 13 at 4:46

Assistant Prof. at Univ. of Pittsburgh


Apr
13
accepted Fubini-Study metric for an infinite dimensional Hilbert space
Apr
13
accepted Weil reciprocity vs Artin reciprocity
Feb
17
comment Interesting behaviour of Brion's formula under a degenerate change of variables
I actually have been interested in very similar (perhaps the same) question some years ago. I think I can give an algebro-geometric (not combinatorial) argument for why the vertices that are not mapped to the vertices of $\phi(P)$ do not appear in the formula, at least for the case of $P =$ a Gelfand-Zetlin polytope. I would be very much interested to know if you have a combinatorial argument in this case.
Feb
17
awarded  Editor
Feb
17
revised Initial ideal of k-th power of an ideal
added 6 characters in body
Feb
17
answered Initial ideal of k-th power of an ideal
Nov
4
comment Continuity of volume of GIT quotients
Thanks a lot Allen.
Oct
29
accepted Continuity of volume of GIT quotients
Oct
27
awarded  Critic
Oct
26
asked Continuity of volume of GIT quotients
Apr
2
comment Fubini-Study metric for an infinite dimensional Hilbert space
Thanks Ahmed and Alvarez, so definition works as in the finite dimensional case.
Mar
30
asked Fubini-Study metric for an infinite dimensional Hilbert space
Mar
25
comment Initial ideal of k-th power of an ideal
Sorry Youngsu for confusion.
Mar
25
comment 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 ${\bf k}$.
Mar
25
comment 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.
Mar
19
asked Initial ideal of k-th power of an ideal
Feb
17
awarded  Yearling
Aug
1
asked Degree of a variety is well-defined
May
9
comment Weil reciprocity vs Artin reciprocity
Thanks guys for the comments. What I meant above is what Dustin also pointed out.
May
8
asked Weil reciprocity vs Artin reciprocity