Principal co-Higgs bundles on \(\mathbb{P}^1\). (English) Zbl 1437.14041
Recall that co-Higgs bundles arise principally in the study of generalized holomorphic bundles on generalized complex manifolds, in the sense of M. Gualtieri [Ann. Math. (2) 174, No. 1, 75–123 (2011; Zbl 1235.32020)] and N. Hitchin [Q. J. Math. 54, No. 3, 281–308 (2003; Zbl 1076.32019)]. Let \(G\) be complex connected reductive affine algebraic groups. The aim of this paper is to give a Lie-theoretic characterization of the semistability of principal \(G\)-co-Higgs bundles on the complex projective line \(\mathbb{P}^1\) in terms of the simple roots of a Borel subgroup of \(G\). The authors describe a stratification of the moduli space in terms of the Harder-Narasimhan type of the underlying bundle. This paper is organized as follows: the first section is an introduction to the subject. The second section deals with adjoint bundle of a co-Higgs bundle and the third section with torus reduction of principal \(G\)-bundles. The forth section concerns a criterion for
stable co-Higgs field. Finally, the fifth section tackles the strata for moduli.
Reviewer: Ahmed Lesfari (El Jadida)
MSC:
| 14H60 | Vector bundles on curves and their moduli |
| 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) |
Keywords:
co-Higgs bundle; principal bundle; projective line; stability; simple roots; moduli; stratificationReferences:
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