On the singular scheme of codimension one holomorphic foliations in P^3

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dc.creatorGiraldo, Luis
dc.creatorPan-Collantes, Antonio J.
dc.date2008-12-17
dc.date.accessioned2026-07-07T12:16:18Z
dc.date.available2026-07-07T12:16:18Z
dc.descriptionIn this work, we begin by showing that a holomorphic foliation with singularities is reduced if and only if its normal sheaf is torsion free. In addition, when the codimension of the singular locus is at least two, it is shown that being reduced is equivalent to the reflexivity of the tangent sheaf. Our main results state on one hand, that the tangent sheaf of a codimension one foliation in P^3 is locally free if and only the singular scheme is a curve, and that it splits if and only if that curve is arithmetically Cohen-Macaulay. On the other hand, we discuss when a split foliation in P^3 is determined by its singular scheme.
dc.descriptionTo appear in the International Journal of Mathematics
dc.identifierhttps://arxiv.org/abs/0812.3369
dc.identifierhttp://arxiv.org/abs/0812.3369
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/211758
dc.subjectAlgebraic Geometry
dc.subjectDynamical Systems
dc.subject14F05, 32S65, 37F75
dc.titleOn the singular scheme of codimension one holomorphic foliations in P^3
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