Orthogonal Higgs bundles with singular spectral curves

TL;DR

This paper explores Higgs bundles associated with non-compact real forms of SO(4,C) and SL(2,C)×SL(2,C), focusing on non-regular fibers in Hitchin fibrations and presenting examples of non-abelian spectral data.

Contribution

It introduces new examples of non-abelian spectral data for specific Higgs bundles related to non-compact real forms and analyzes non-regular fibers in Hitchin fibrations.

Findings

Identification of non-regular fibers in Hitchin fibrations.

Construction of non-abelian spectral data examples.

Insights into Higgs bundles for non-compact real forms.

Abstract

We examine Higgs bundles for non-compact real forms of SO(4,C) and the isogenous complex group SL(2,C)XSL(2,C). This involves a study of non-regular fibers in the corresponding Hitchin fibrations and provides interesting examples of non-abelian spectral data.