Timeline for Hodge-Index Theorem for $\mathbb{C}P^2$
Current License: CC BY-SA 2.5
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 16, 2009 at 20:28 | comment | added | Ilya Nikokoshev | @John: it might be a good idea to post another question -- more people will be able to answer that way. | |
| Nov 16, 2009 at 20:11 | vote | accept | John McCarthy | ||
| Nov 16, 2009 at 19:09 | comment | added | David E Speyer | Don't have time to do G(k,n) in general. Here's a small example: H^4(G(2,4)) is spanned by two Schubert classes: X:=[20] and Y:=[11]. The pairing on them has matrix ((0,1),(1,0)). Taking omega to be the chern class of the standard Plucker embedding, omega^2 H^0 is spanned by X+Y. Also, omega H^1 is spanned by X+Y. The statement should be that the pairing is positive definite on omega^2 H^0 and negative definite on the orthogonal complement of omega H^1 (namely, X-Y). I think I might have gotten some of the signs wrong in my previous write up of this; I'll check later. | |
| Nov 16, 2009 at 18:45 | vote | accept | John McCarthy | ||
| Nov 16, 2009 at 18:45 | |||||
| Nov 16, 2009 at 18:40 | comment | added | John McCarthy | .... and for the complex Grassamnnian Gr(n,k)? | |
| Nov 16, 2009 at 18:36 | history | answered | David E Speyer | CC BY-SA 2.5 |