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Principal co-Higgs bundles on ℙ1

Part of: Curves Families, fibrations

Published online by Cambridge University Press:  05 March 2020

Indranil Biswas ,
Oscar García-Prada ,
Jacques Hurtubise  and
Steven Rayan
Indranil Biswas
Affiliation:
School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai400005, India (indranil@math.tifr.res.in)
Oscar García-Prada
Affiliation:
ICMAT (Instituto de Ciencias Matemáticas), Calle Nicolás Cabrera, no. 13–15, Campus Cantoblanco, 28049Madrid, Spain (oscar.garcia-prada@icmat.es)
Jacques Hurtubise
Affiliation:
Department of Mathematics & Statistics, McGill University, Burnside Hall, 805 Sherbrooke Street West, Montréal, QC, CanadaH3A 0B9 (jacques.hurtubise@mcgill.ca)
Steven Rayan
Affiliation:
Centre for Quantum Topology and Its Applications (quanTA) and Department of Mathematics & Statistics, University of Saskatchewan, McLean Hall, 106 Wiggins Road, Saskatoon, SK, CanadaS7N 5E6 (rayan@math.usask.ca)
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Abstract

For complex connected, reductive, affine, algebraic groups G, we give a Lie-theoretic characterization of the semistability of principal G-co-Higgs bundles on the complex projective line ℙ1 in terms of the simple roots of a Borel subgroup of G. We describe a stratification of the moduli space in terms of the Harder–Narasimhan type of the underlying bundle.

Keywords

co-Higgs bundleprincipal bundleprojective linestabilitysimple rootsmodulistratification

MSC classification

Primary: 14H60: Vector bundles on curves and their moduli
Secondary: 14D20: Algebraic moduli problems, moduli of vector bundles 14D21: Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory)
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 63 , Issue 2 , May 2020 , pp. 512 - 530
Copyright
Copyright © Edinburgh Mathematical Society 2020

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