Vector Fields on Smooth Threefolds Vanishing on Complete Intersections

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dc.creatorEckl, Thomas
dc.date2001-04-24
dc.date.accessioned2026-07-07T04:41:25Z
dc.date.available2026-07-07T04:41:25Z
dc.descriptionThe existence of a vector field on a compact Kaehler manifold with nonempty zero locus and the properties of this zero locus strongly influence the geometry of the manifold. For example, J. Wahl proved that the existence of a vector field vanishing on an ample divisor of a projective normal variety X implies that X is a cone over this divisor. If X is smooth, X will be isomorphic to the n-dimensional projective space. This paper is a first attempt to generalize Wahl's theorem to higher codimensions: Given a complex smooth projective threefold X and a vector field on X vanishing on an irreducible and reduced curve which is the scheme theoretic intersection of two ample divisors, X is isomorphic to the 3-dimensional projective space or the 3-dimensional quadric.
dc.description11 pages
dc.identifierhttps://arxiv.org/abs/math/0104217
dc.identifierhttp://arxiv.org/abs/math/0104217
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/61349
dc.subjectAlgebraic Geometry
dc.subject14M20 (Primary), 14L99, 14F05 (Secondary)
dc.titleVector Fields on Smooth Threefolds Vanishing on Complete Intersections
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