Branching of Hitchin's Prym cover for SL(2)

TL;DR

This paper investigates the branching behavior of Hitchin's Prym cover for SL(2), revealing that the spectral curve Jacobian map is generically simply branched, which challenges previous assumptions in related abelianization methods.

Contribution

It demonstrates that the spectral curve Jacobian map is generically simply branched, contradicting a key step in prior abelianization approaches for the SU(2) WZW connection.

Findings

The map from the spectral curve Jacobian to stable bundles is generically simply branched.

This branching occurs along an irreducible divisor.

The result falsifies a previous key assumption in abelianization methods.

Abstract

It is shown that the map from the Jacobian of the spectral curve to the moduli of stable bundles of rank 2 is generically simply branched along an irreducible divisor. This observation falsifies the key step in the "abelianization of the SU(2) WZW connection" presented in a recent paper [Yoshida, Annals 2006]