The nilpotent cone in the Mukai system of rank two and genus two

Abstract: Let $S$ be a K3 surface and $C$ a smooth curve in $S$. We consider the moduli space $M$ of coherent sheaves on $S$ which are supported on a curve rational equivalent to $nC$ and have fixed Euler characteristic (coprime to $n$). Then $M$ is an irreducible holomorphic symplectic manifold equipped with a Lagrangian fibration given by taking supports. This is the beautiful Mukai system.

One source of interest in the Mukai system is, that it deforms to the Hitchin system on $C$. And there is a notion of the nilpotent cone in the Mukai system deforming to the nilpotent cone in the Hitchin system. In my talk, I present some results about the nilpotent cone on the Mukai side (in the lowest dimensional case), which can then be transferred to the Hitchin side.

mathematical physicsalgebraic geometrydifferential geometrygeometric topologyoperator algebrasrepresentation theorysymplectic geometry

Audience: researchers in the topic

Geometry, Physics, and Representation Theory Seminar

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