Abstract Let X X be a compact Riemann surface of genus g ≥ 2 g 2. The geometry of the moduli space ℳ (Spin (8, C) ) { M } (Spin (8, C) ) of Spin (8, C) Spin (8, C) -Higgs bundles over X X is of great interest both in algebraic geometry and mathematical physics. Consequently, several works have studied subvarieties of fixed points of this moduli space, especially those arising from the automorphism induced by the action of triality. In this work, fixed points of automorphisms of ℳ (Spin (8, C) ) { M } (Spin (8, C) ) induced by outer automorphisms of Spin (8, C) Spin (8, C) are studied. This is done by giving explicit descriptions of the spectral data of these fixed points induced by the Hitchin fibration, under certain technical conditions that must be required. Specifically, it is proved that stable Spin (8, C) Spin (8, C) -Higgs bundles that admit nontrivial automorphisms reduce their structure group to a subgroup isomorphic to SL (2, C) 4 = SL (2, C) × SL (2, C) × SL (2, C) × SL (2, C) SL (2, {C) }^4=SL (2, C) SL (2, C) SL (2, C) SL (2, C). Subsequently, the spectral data of these reductions are described and the manner in which the outer automorphisms of Spin (8, C) Spin (8, C) act on them is analyzed. The final application of these results allows a description of the mentioned fixed points through their spectral data.
Álvaro Antón‐Sancho (Wed,) studied this question.