Higgs bundles on weighted projective lines and loop crystals

Abstract

We consider the space of nilpotent Higgs bundles on a weighted projective line, as a global analog of the nilpotent cone. We show that it is pure, compute its dimension, and define geometric correspondences between irreducible components. We prove it by constructing a loop analog of a cristal, in the spirit of Kashiwara and Saito, for some corresponding loop Kac-Moody algebra.

Contains generalizations of some results of arXiv:1005.3732

References in corpus (3)

• Stability conditions and Stokes factors
• The moduli stack of parabolic bundles over the projective line, quiver representations, and the Deligne-Simpson problem
• Canonical bases of loop algebras via quot schemes II