Timeline for Computing quantum cohomology for total spaces of vector bundles over $\mathbb{P}^m$
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
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| Feb 29, 2016 at 14:54 | vote | accept | YHBKJ | ||
| Feb 20, 2016 at 9:40 | answer | added | Honglu | timeline score: 4 | |
| Oct 20, 2015 at 0:50 | comment | added | Allen Knutson | I'm guessing the natural equivariance is w.r.t. $T^n$, though obviously bigger groups act. | |
| Oct 18, 2015 at 13:37 | comment | added | YHBKJ | @JasonStarr I'm talking about GW invariants taking values in cohomology. There may still be some non-trivial GW invariants, and when the rank of the bundle is not small compared to the dimension of the case, I think the computaton of $QH$ will still be involved as there are potentially many non-trivial GW invariants. | |
| Oct 18, 2015 at 13:31 | comment | added | Jason Starr | Regarding Allen's question: are you asking about Gromov-Witten invariants taking values in cohomology / Chow theory, or are you asking about equivariant Gromov-Witten invariants for equivariant cohomology / equivariant Gromov-Witten theory. When $n\gg m$, of course the "usual" Gromov-Witten invariants are zero, while the equivariant theory can be nonzero. If you are asking about equivariant invariants, what is your choice of group action? | |
| Oct 18, 2015 at 7:51 | comment | added | pro | the question made me think of this paper, but I have no idea whether it's relevant (thought I'd share anyway) projecteuclid.org/euclid.nmj/1415383898 | |
| Oct 18, 2015 at 3:26 | history | edited | YHBKJ | CC BY-SA 3.0 |
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| Oct 18, 2015 at 3:10 | history | edited | YHBKJ | CC BY-SA 3.0 |
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| Oct 18, 2015 at 3:06 | comment | added | YHBKJ | @AllenKnutson Sure. | |
| Oct 17, 2015 at 20:24 | comment | added | Allen Knutson | Naive question: since these bundles have no sections, won't any holomorphic curves all land in the base $\mathbb P^m$? | |
| Oct 17, 2015 at 19:10 | history | asked | YHBKJ | CC BY-SA 3.0 |