RT Journal Article
T1 On the singular scheme of codimension one holomorphic foliations in P(3)
A1 Giraldo Suárez, Luis
A1 Pan-Collantes, Antonio J.
AB 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.
PB World Scientific Publishing
SN 0129-167X
YR 2010
FD 2010
LK https://hdl.handle.net/20.500.14352/42301
UL https://hdl.handle.net/20.500.14352/42301
LA eng
NO Plan Nacional I+D
NO Ministerio de Educación y Ciencia (España)
DS Docta Complutense
RD 6 jun 2025