Timeline for Intersection of subvarieties in grassmannian space
Current License: CC BY-SA 2.5
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 15, 2011 at 11:44 | vote | accept | Jairo Bochi | ||
| Jan 17, 2011 at 6:12 | |||||
| Jan 15, 2011 at 9:59 | history | edited | Francesco Polizzi | CC BY-SA 2.5 |
added 2 characters in body
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| Jan 14, 2011 at 14:46 | comment | added | Jairo Bochi | Ok. I think I can reread this as follows (applying back the isomorphism): Take a splitting $\C^4 = E \oplus F$ where $\dim E = 1$, $\dim F = 3$. Take $Y$ (resp. $X$) as the set of $2$-spaces of $\C^4$ that contain $E$ (resp. are contained in $F$). Then $X$ and $Y$ are disjoint and $\dim X + \dim Y = 2 + 2 = \dim G(2,4)$. Thank you very much. Any idea about the second question? | |
| Jan 14, 2011 at 14:36 | comment | added | Francesco Polizzi | Dear Allen, I think this is really a standard counterexample. I was just lucky to sit in front of my computer at the right moment :-) | |
| Jan 14, 2011 at 14:32 | comment | added | Allen Knutson | Gah, too slow writing the same counterexample. Anyway the basic point is that the Betti numbers of projective space are all 1, but $b_4$ of G(2,4) is 2, with $\Sigma_p,\Sigma_H$ giving a basis. | |
| Jan 14, 2011 at 14:28 | history | answered | Francesco Polizzi | CC BY-SA 2.5 |