Timeline for Core components of quiver varieties as fiber bundles of flag varieties
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Feb 15, 2019 at 0:48 | comment | added | Hiraku Nakajima | The condition that all core components are smooth sounds very restrictive. The corresponding result for Springer fibers in type A is link.springer.com/article/10.1007%2Fs00029-010-0025-z. I do not know how much other examples one get from Spaltenstein varieties = core of type A quiver varieties. I did not study other components in the above E6 example. So I do not know whether it satisfies the condition or not. | |
| Feb 13, 2019 at 22:36 | comment | added | Filip | I see, many thanks! So, I guess I should really think of this statement as a feature of type A quiver varieties? | |
| Feb 13, 2019 at 13:44 | comment | added | Hiraku Nakajima | Oh, sorry. There are examples of blowup of $\mathbb P^2$ at three points in E6 constructed in similar way as this example, as far as I remember. I guess, you could also find them by running my computer program in arxiv.org/pdf/math/0606637.pdf. | |
| Feb 13, 2019 at 10:37 | comment | added | Filip | Indeed, but blowup of $\mathbb{P}^2$ at a point is a Hirzebruch surface $\mathbb{F}_1$ hence a (non-trivial) $\mathbb{P}^1$ bundle over $\mathbb{P}^1.$ | |
| Feb 13, 2019 at 2:36 | history | answered | Hiraku Nakajima | CC BY-SA 4.0 |