Timeline for How Gr(2,7) and Gr(3,6) are related?
Current License: CC BY-SA 3.0
14 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 8, 2011 at 1:40 | comment | added | Allen Knutson | In each case, you could compute their multigraded Hilbert series; these are of course different because they involve a different number of variables. But then it would be worth knowing if the second one is a specialization of the first, or how drastically you have to specialize each of their variables before the series agree. The point being that it would constrain what sort of degeneration (for David and David) to look for, i.e. how equivariant one might hope the degeneration to be. | |
| Nov 7, 2011 at 13:05 | comment | added | Sasha | @M I - Now I understand that the numerators are identical and the denominators differ by the factor $(1-t)$. | |
| Nov 7, 2011 at 12:36 | comment | added | M I | @Sasha....did you find it of any use at all? | |
| Nov 4, 2011 at 23:12 | comment | added | M I | @Sasha..In fact the Hilbert numerator is $1-35t^2+140t^3-189t^4-112t^5+735t^6-1080t^7+735t^8-112t^9-189t^{10}+140t^{11}-35t^{12}+t^{14},$ for both varieites. The denomenator is obviously $(1-t)^{21}$ and $(1-t)^{20}$. | |
| Nov 4, 2011 at 22:52 | vote | accept | M I | ||
| Nov 4, 2011 at 16:18 | history | edited | M I | CC BY-SA 3.0 |
deleted 5 characters in body
|
| Nov 4, 2011 at 9:21 | comment | added | Sasha | @M I - I mean, what is the precise relation between the numerators and denominators of Hilbert series? | |
| Nov 3, 2011 at 20:17 | answer | added | Dave Anderson | timeline score: 1 | |
| Nov 3, 2011 at 18:31 | comment | added | David E Speyer | I know what I want the answer to be. Let $\Delta$ be the Schubert divisor in $G(2,7)$ -- this is the set of $2$-planes in $7$-space which meet a fixed $5$-plane nontransversely. This is a hyperplane section of $G(2,7)$. I want there to be a flat degeneration from $G(3,6)$ to $\Delta$. No idea about how to find it though... | |
| Nov 3, 2011 at 17:43 | comment | added | M I | @Sasha.. Sorry, I Didn't get what exactly may I let you know about them? | |
| Nov 3, 2011 at 16:55 | comment | added | Sasha | Can you give more details on these Hilbert series? | |
| Nov 3, 2011 at 16:54 | answer | added | Sasha | timeline score: 9 | |
| Nov 3, 2011 at 16:35 | answer | added | algori | timeline score: 11 | |
| Nov 3, 2011 at 15:50 | history | asked | M I | CC BY-SA 3.0 |