Timeline for Hitchin fibration and Springer resolution
Current License: CC BY-SA 3.0
19 events
| when toggle format | what | by | license | comment | |
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| Oct 17, 2017 at 20:48 | answer | added | Aswin | timeline score: 5 | |
| Aug 24, 2017 at 11:46 | answer | added | Niels | timeline score: 7 | |
| Jul 31, 2017 at 20:50 | comment | added | Niels | @Satoshi Nawata I will try to answer the first question if no answer is given but only in a few days since I am not able right now. | |
| Jul 31, 2017 at 18:44 | history | edited | Satoshi Nawata | CC BY-SA 3.0 |
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| Jul 31, 2017 at 18:44 | comment | added | Satoshi Nawata | @Niels Thank you very much for the references. I keep your suggestion in mind. But I have already posted this question. This time let's see whether people can give me some hints or answers to at least one of questions. I would be nice if you could elaborate BNR correspondence or Laumon's work indeed. | |
| Jul 30, 2017 at 17:28 | comment | added | Niels | In the definition of the Hitchin map, the direct sum starts at $i=1$. | |
| Jul 30, 2017 at 17:27 | comment | added | Niels | For your second question, probably the reference is : Laumon, Un analogue global du cône nilpotent. Duke Math. J. 57 (1988), no. 2, 647–671. projecteuclid.org/euclid.dmj/1077307053 | |
| Jul 30, 2017 at 17:03 | comment | added | Niels | I would say your question is too broad, it would be better to split it into three distinct questions, you will get better answers. | |
| Jul 30, 2017 at 16:52 | comment | added | Niels | `does the spectral curve of C degenerate into a nodal curve and is the singular fiber a compactified Jacobian' : yes, by the same BNR correspondence. Beauville, Narasimhan, Ramanan, Spectral curves and the generalised theta divisor. J. Reine Angew. Math. 398 (1989), 169–179. doi.org/10.1515/crll.1989.398.169 | |
| Jul 30, 2017 at 12:47 | comment | added | Satoshi Nawata | @Niels Thanks for pointing out my mistake. I have corrected it. | |
| Jul 30, 2017 at 12:45 | history | edited | Satoshi Nawata | CC BY-SA 3.0 |
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| Jul 30, 2017 at 12:34 | comment | added | Niels | `The Hitchin fibration is a completely integrable system and a generic fiber is the Jacobian of $C$ which is a Lagrangian complex tori.': this is wrong, this is instead the Jacobian of the corresponding spectral curve which is a degree $N$ cover of $C$. This is called the BNR correspondence. | |
| Jul 30, 2017 at 8:53 | comment | added | Peter Dalakov | A generic spectral curve in the discriminant locus has a single ODP, see Kouvidakis-Pantev, Remark 1.7 and further. | |
| Jul 30, 2017 at 8:51 | history | edited | Satoshi Nawata | CC BY-SA 3.0 |
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| Jul 30, 2017 at 7:24 | comment | added | მამუკა ჯიბლაძე | Related: What do the components of the global nilpotent cone look like? | |
| Jul 30, 2017 at 6:36 | history | edited | Satoshi Nawata | CC BY-SA 3.0 |
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| Jul 30, 2017 at 6:16 | comment | added | Jingren Chi | For question 2, let $\chi: g\to c$ be the "characteristic polynomial" map, then the nilpotent cone is $\chi^{-1}(0)$. The Hitchin fibration $\pi$ is a global analogue of $\chi$. So $\pi^{-1}(0)$ may be viewed as "global nilpotent cone". | |
| Jul 30, 2017 at 5:52 | history | edited | ThiKu | CC BY-SA 3.0 |
minor typos
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| Jul 30, 2017 at 5:41 | history | asked | Satoshi Nawata | CC BY-SA 3.0 |