Poisson geometry of parabolic bundles on Elliptic curves

2006/07/03 by David Balduzzi, Balduzzi, David
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Homotopy and Cohomology in Algebraic Topology #math.AG #math.SG #msc:14H60 #msc:53D17 #msc:53D20

paper · pdf · doi:10.48550/arxiv.math/0607061

Final version: typos fixed, some re-organization; to appear IJM

arxiv created 2007/11/17 · arxiv updated 2009/12/01

Abstract

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 methods and for the case \SL₂ perform explicit computations, describing the bracket and its leaves in detail.

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