| The Donagi-Markman cubic is the differential of the period map for algebraic completely integrable systems. We investigate the cubic in the case where the lagrangian fibers are not polarized. We then specialize to the Hitchin system where we prove a formula for the cubic for arbitrary g . This was originally stated (without proof) by Pantev for sln .;The moduli space of G-bundles on an elliptic curve with additional flag structure admits a Poisson structure. The bivector can be defined using double loop group, loop group and sheaf cohomology constructions. We investigate the links between these constructions and for the case of SL 2 perform explicit computations, describing the bracket and its leaves in detail. |
