Spin(8,C)-Higgs pairs over a compact Riemann surface

Antón-Sancho, Álvaro (2023) Spin(8,C)-Higgs pairs over a compact Riemann surface. Open Mathematics, 21 (1). ISSN 2391-5455

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Abstract

Let X be a compact Riemann surface of genus g≥2 , G be a semisimple complex Lie group and ρ:G→GL(V) be a complex representation of G . Given a principal G -bundle E over X , a vector bundle E(V) whose typical fiber is a copy of V is induced. A (G,ρ) -Higgs pair is a pair (E,φ) , where E is a principal G -bundle over X and φ is a holomorphic global section of E(V)⊗L , L being a fixed line bundle over X . In this work, Higgs pairs of this type are considered for G=Spin(8,C) and the three irreducible eight-dimensional complex representations which Spin(8,C) admits. In particular, the reduced notions of stability, semistability, and polystability for these specific Higgs pairs are given, and it is proved that the corresponding moduli spaces are isomorphic, and a precise expression for the stable and not simple Higgs pairs associated with one of the three announced representations of Spin(8,C) is described.

Item Type:	Article
Subjects:	MSC 2010, the AMS's Mathematics Subject Classification > 14 Algebraic geometry
Depositing User:	Dr. Álvaro Antón-Sancho
Date Deposited:	03 Feb 2024 20:18
Last Modified:	03 Feb 2024 20:18
URI:	https://eprints.maths.manchester.ac.uk/id/eprint/2889

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