Symmetric differentials and the dimension of Hitchin components for orbi-curves

TL;DR

This paper explores the dimension of Hitchin components for orbifold groups by applying the orbifold Riemann-Roch theorem, providing an expository account of joint work and recasting it in the language of analytic orbi-curves.

Contribution

It introduces a new approach to compute Hitchin component dimensions for orbifold groups using orbifold Riemann-Roch, connecting geometric analysis with orbifold theory.

Findings

Dimension of Hitchin components computed via orbifold Riemann-Roch

Recasting of Hitchin component analysis in the language of analytic orbi-curves

Simplification of dimension calculations for orbifold groups

Abstract

This note is based on a talk given at the 2019 ISAAC Congress in Aveiro, Portugal. We give an expository account of joint work with Daniele Alessandrini and Gye-Seon Lee on Hitchin components for orbifold groups (arXiv:1811.05366), recasting part of it in the language of analytic orbi-curves. This reduces the computation of the dimension of the Hitchin component for orbifold groups to an application of the orbifold Riemann-Roch theorem.