Timeline for What is the relationship between integrable systems and toric degenerations?
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| Jan 26, 2010 at 3:37 | comment | added | Allen Knutson | Well, one issue is that an integrable system may have no action variables, because there may be monodromy in choosing them -- Duistermaat shows that this actually occurs for the double pendulum, I think. (Look up Duistermaat in "Symplectic techniques in physics" [GS].) So no polytope, no toric variety to try to degenerate to. One can ask for less than an integrable system -- just some commmuting Hamiltonians (e.g. from the Thimm trick) -- and less than a toric degeneration -- just a degeneration picking up some new symmetry (e.g. the Vinberg asymptotic cone). GCSGL is iterated from these. | |
| Jan 25, 2010 at 23:03 | comment | added | David Treumann | This is great. I didn't know the total space of the GCSGL degeneration was not smooth. What do you know about going in the other direction? i.e. stealing a toric degeneration from an integrable system. | |
| Jan 24, 2010 at 1:17 | history | answered | Allen Knutson | CC BY-SA 2.5 |