Algebraic and hamiltonian approaches to isostokes deformations

Details Algebraic and hamiltonian approaches to isostokes deformations Algebraic and hamiltonian approaches to isostokes deformations

2004-12-06

arxiv.org/abs/math/0412121v3

Transformation Groups, Volume 11, Number 2 / June, 2006

Mathematics

Algebraic Geometry

23 pages, minor corrections in the introduction, references expanded

Scientific paper

10.1007/s00031-005-1107-4

We study a generalization of the isomonodromic deformation to the case of connections with irregular singularities. We call this generalization Isostokes Deformation. A new deformation parameter arises: one can deform the formal normal forms of connections at irregular points. We study this part of the deformation, giving an algebraic description. Then we show how to use loop groups and hypercohomology to write explicit hamiltonians. We work on an arbitrary complete algebraic curve, the structure group is an arbitrary semisimiple group.

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