Minitwistor spaces, Severi varieties, and Einstein-Weyl structure

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dc.creatorHonda, Nobuhiro
dc.creatorNakata, Fuminori
dc.date2009-01-15
dc.date.accessioned2026-07-07T12:30:31Z
dc.date.available2026-07-07T12:30:31Z
dc.descriptionIn this paper we show that the space of nodal rational curves, which is so called a Severi variety (of rational curves), on any non-singular projective surface is always equipped with a natural Einstein-Weyl structure, if the space is 3-dimensional. This is a generalization of the Einstein-Weyl structure on the space of smooth rational curves on a complex surface, given by N.Hitchin. As geometric objects naturally associated to Einstein-Weyl structure, we investigate null surfaces and geodesics on the Severi varieties. Also we see that if the projective surface has an appropriate real structure, then the real locus of the Severi variety becomes a positive definite Einstein-Weyl manifold. Moreover we construct various explicit examples of rational surfaces having 3-dimensional Severi varieties of rational curves.
dc.description30 pages
dc.identifierhttps://arxiv.org/abs/0901.2264
dc.identifierhttp://arxiv.org/abs/0901.2264
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/216154
dc.subjectDifferential Geometry
dc.subjectAlgebraic Geometry
dc.subject32L25;
dc.titleMinitwistor spaces, Severi varieties, and Einstein-Weyl structure
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