Jordan-Hölder theory for complementary polyhedra and moduli of parahoric Higgs torsors
Emanuel Roth
Source abstract
We extend Behrend's theory of complementary polyhedra to include Jordan-Hölder theory. This provides a uniform approach to describing the Jordan-Hölder filtrations and S-equivalence in moduli stacks of bundles, following Zhang. As an application, we give a description of Jordan-Hölder reductions and S-equivalence in the semistable locus of parahoric torsors and parahoric Higgs torsors, coming from their good moduli spaces constructed by Alper-Halpern-Leistner-Heinloth and Réga. This application uses the Rees construction to identify filtrations of moduli stacks with reductions of bundles, and induces a Jordan-Hölder stratification of the moduli stacks.
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