Hyperelliptic curves and Hitchin tangential covers

TL;DR

This paper extends tangency conditions from elliptic solitons to Hitchin systems, defining Hitchin hyperelliptic tangential covers and proving their finiteness within all Hitchin tangential covers.

Contribution

It introduces Hitchin hyperelliptic tangential covers and establishes their finiteness, generalizing previous elliptic soliton tangency conditions to Hitchin systems.

Findings

Defined Hitchin hyperelliptic tangential covers

Proved finiteness of these covers among all Hitchin tangential covers

Extended tangency conditions from elliptic solitons to Hitchin systems

Abstract

In \cite{kim11} we have generalized a tangency condition in the Treibich-Verdier theory \cite{trei89,tv90,trei97} about elliptic solitons to a Hitchin system. As an application of this generalization, we will define, so-called, Hitchin hyperelliptic tangential covers and show the finiteness of them among all Hitchin tangential covers.