publication . Article . Preprint . Other literature type . 2014

CONSTRUCTING CO-HIGGS BUNDLES ON ℂℙ2

Rayan, S.;
Open Access
  • Published: 11 Jul 2014 Journal: The Quarterly Journal of Mathematics, volume 65, pages 1,437-1,460 (issn: 0033-5606, eissn: 1464-3847, Copyright policy)
  • Publisher: Oxford University Press (OUP)
Abstract
On a complex manifold, a co-Higgs bundle is a holomorphic vector bundle with an endomorphism twisted by the tangent bundle. The notion of generalized holomorphic bundle in Hitchin's generalized geometry coincides with that of co-Higgs bundle when the generalized complex manifold is ordinary complex. Schwarzenberger's rank-2 vector bundle on the projective plane, constructed from a line bundle on the double cover CP^1 \times CP^1 \to CP^2, is naturally a co-Higgs bundle, with the twisted endomorphism, or "Higgs field", also descending from the double cover. Allowing the branch conic to vary, we find that Schwarzenberger bundles give rise to an 8-dimensional modul...
Subjects
arXiv: Mathematics::Symplectic GeometryMathematics::Algebraic GeometryHigh Energy Physics::PhenomenologyHigh Energy Physics::Experiment
free text keywords: General Mathematics, Vector bundle, Connection (principal bundle), Mathematical analysis, Holomorphic vector bundle, Principal bundle, Connection (vector bundle), Topology, Frame bundle, Line bundle, Normal bundle, Mathematics, Mathematics - Algebraic Geometry, Mathematics - Differential Geometry
Related Organizations
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publication . Article . Preprint . Other literature type . 2014

CONSTRUCTING CO-HIGGS BUNDLES ON ℂℙ2

Rayan, S.;