Timeline for conformal blocks for beginners
Current License: CC BY-SA 3.0
9 events
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| Dec 5, 2012 at 17:39 | comment | added | Peter Dalakov | Right, of course, you then have to work with bundles on singular curves. Though I think there has been work in that direction. (There was a paper of I.Kausz on this, I believe). But at least you will have a well-motivated (for AG-ers) description in the interior. | |
| Dec 5, 2012 at 8:49 | comment | added | IMeasy | No that's ok, but the problem is then explaining the degeneration over the boundary. To my knowledge there's no real satisfactory way of degenerating the generalized theta functions interpretation, am I wrong? | |
| Dec 4, 2012 at 11:19 | comment | added | Peter Dalakov | Have you tried starting with the "obvious" introduction/motivation: the moduli of vector bundles of fixed det,coprime rank & deg (and n=0) when the coarse moduli space is smooth, with $Pic\simeq \mathbb{Z}$. You can then discuss the Verlinde bundle over Teichmueller space. If you want to be really concrete, you can mention e.g. rank 2 bundles of degree zero and fixed determinant for $g=2$, when the coarse moduli space is $\mathbb{P}^3$. And then you can say that you want to upgrade this to a fancier version, living on $\overline{\mathcal{M}}_{g,n}$? Or is this too trivial for your audiences? | |
| Dec 3, 2012 at 17:13 | comment | added | IMeasy | I am sorry I did not mention: the hypothesis is "public of algebraic geometers, with some knowledge of moduli spaces, but zero knowledge of CB". this is the enviromment I find the most difficult. | |
| Dec 3, 2012 at 16:50 | comment | added | stankewicz | Ah, read Beauville! I found this paper math.unice.fr/~beauvill/pubs/Hirz65.pdf to be most helpful, but this may just be my own preference towards Lie algebras. He also has several papers which give a "generalized theta function" approach. | |
| Dec 3, 2012 at 15:50 | history | edited | IMeasy |
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| Dec 3, 2012 at 15:49 | comment | added | IMeasy | I approached CB mainly as vector bundles on the moduli of curves, as spaces of generalized theta functions on the moduli of bundles on curves, but the only definition working also on the boundary that I know is the one as sheaves of covacua. | |
| Dec 3, 2012 at 15:44 | comment | added | stankewicz | Conformal blocks can of course be approached in lots of different ways which are more or less intelligible to different groups of people. Could you tell us more about your background or the background of the audience you'd like to present to? | |
| Dec 3, 2012 at 13:22 | history | asked | IMeasy | CC BY-SA 3.0 |