A Non-Linear Deformation of the Hitchin Dynamical System

Details A Non-Linear Deformation of the Hitchin Dynamical System A Non-Linear Deformation of the Hitchin Dynamical System

1995-04-30

arxiv.org/abs/alg-geom/9504017v1

Mathematics

Algebraic Geometry

Scientific paper

Mukai's space, parametrizing simple sheaves on a K3 surface S whose numerical invariants are those of a line bundle on a curve C in S, is interpreted as a deformation of Hitchin's system on C. This is used to show that the nilpotent cone in Mukai space is Lagrangian. In rank 2, components of this nilpotent cone are described as affine bundles over symmetric products of the curve. The underlying vector bundles give the corresponding components of the Hitchin nilpotent cone.

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