ADE-bundles over rational surfaces, configuration of lines and rulings

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dc.creatorLeung, Naichung Conan
dc.date2000-09-20
dc.date.accessioned2026-07-07T04:37:37Z
dc.date.available2026-07-07T04:37:37Z
dc.descriptionTo each del Pezzo surface (resp. ruled surface, ruled surface with a section), we describe a natural Lie algebra bundle of type E_n (resp. D_n, A_n) over it. Using lines and rulings on any such surface, we describe various representation bundles corresponding to fundamental representations of the corresponding Lie algebra. When we specify a geometric structure on the surface to reduce the Lie algebra to a smaller one, then the classical geometry of the configuration of lines and rulings is encoded beautifully by the branching rules in Lie theory. We discuss this relationship in details. When we degenerate the surface to a non-normal del Pezzo surface, we discover that the configurations of lines and rulings are also governed by certain branching rules.
dc.description61 pages
dc.identifierhttps://arxiv.org/abs/math/0009192
dc.identifierhttp://arxiv.org/abs/math/0009192
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/59972
dc.subjectAlgebraic Geometry
dc.subjectRepresentation Theory
dc.titleADE-bundles over rational surfaces, configuration of lines and rulings
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