Generic Fibers of Parahoric Hitchin Systems

TL;DR

This paper studies the geometry of generic fibers in parahoric Hitchin systems over smooth projective curves, generalizing previous work on GLn, using root stacks to describe their structure.

Contribution

It provides a geometric description of generic fibers of parahoric Hitchin fibrations, extending known results to a broader class of groups using root stacks.

Findings

Describes the geometry of generic fibers using root stacks

Generalizes the GLn case to semisimple simply connected groups

Works over algebraically closed fields with mild characteristic assumptions

Abstract

In this paper, we talk about parahoric Hitchin systems over smooth projective curves with structure group a semisimple simply connected group. We describe the geometry of generic fibers of parahoric Hitchin fibrations using root stacks. We work over an algebraically closed field with a mild assumption of the characteristic. All of these can be treated as a generalization of GLn case in [SWW19]