Self-duality of of reducible GL(n) Hitchin fibers
This is a report on a joint work in progress with D.Arinkin. We investigate the self-duality question for the compactified stacky Jacobian of a reducible curve with planar singularities. This is needed for extending the classical limit Langlands duality for GL(n) to the whole moduli of Higgs bundles. I will explain how the self-duality statement extends to a single reduced but possibly reducible curve and will discuss the technical issues that one needs to overcome to prove the statement in families. I will also discuss the way self-duality interacts with stability.