Timeline for Does the moduli space of smooth curves of genus g contain an elliptic curve
Current License: CC BY-SA 3.0
6 events
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| Aug 2, 2012 at 11:19 | comment | added | inkspot | @Jim: sometimes the coarse space is all you have. E.g., both the stack and the coarse space of $g$-dimensional ppav's have toroidal compactifications, but, for $g>1$, only the coarse space has a Satake compactification. It is this compactification that Faltings uses to prove the Mordell conjecture because it is here that there exists an ample line bundle with a good height function. More broadly, Mumford asks [GIT, ch. 5, l. 1] "What are moduli?", then gives no definitive answer, despite having already written the first paper to take stacks seriously as geometric objects. | |
| Jul 26, 2012 at 12:42 | comment | added | Arend Bayer | Does that mean that the moduli stack of super-Riemann surfaces might be split? If so, why do Donagi-Witten care whether the moduli space is split? (Sorry for getting off-topic.) | |
| Jul 26, 2012 at 5:42 | comment | added | Eric Zaslow | Jim, if I understood their talks correctly, your old result was just used by Donagi and Witten to show that the moduli space of super-Riemann surfaces does not split -- meaning superstring perturbation theory itself needs to be "revisited." | |
| Jul 26, 2012 at 3:33 | comment | added | Jim Bryan | It was just pointed out to me by a friend that if you are studying the MMP program for $M_g$ (which is certainly an interesting endeavour), then you are more interested in the geometry of the coarse space. So maybe I need to walk back my flippant comment! | |
| Jul 26, 2012 at 2:03 | comment | added | roy smith | Jim I love this: "why would you be interested in the coarse space?"! | |
| Jul 26, 2012 at 1:14 | history | answered | Jim Bryan | CC BY-SA 3.0 |