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

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Giraldo Suárez, Luis and Pan-Collantes, Antonio J. (2010) On the singular scheme of codimension one holomorphic foliations in P(3). International Journal of Mathematics, 21 (7). pp. 843-858. ISSN 0129-167X

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Official URL: http://www.worldscinet.com/ijm/21/2107/S0129167X1000601X.html


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Abstract

In 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 P3 is locally free if and only if the singular scheme is a curve, and that it splits if and only if it is arithmetically Cohen–Macaulay. On the other hand, we discuss when a split foliation in P3 is determined by its singular scheme.


Item Type:Article
Uncontrolled Keywords:Holomorphic foliations; reflexive sheaves; split vector bundles
Subjects:Sciences > Mathematics > Algebraic geometry
ID Code:16332
Deposited On:12 Sep 2012 10:59
Last Modified:12 Dec 2018 15:13

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