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

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]
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Algebra and Geometry · Algebraic structures and combinatorial models
