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On holomorphic distributions on Fano threefolds. (English) Zbl 1439.57047
Summary: This paper is devoted to the study of holomorphic distributions of dimension and codimension one on smooth weighted projective complete intersection Fano manifolds \(X\) which is threedimensional and with Picard number equal to one. We study the relations between algebro-geometric properties of the singular set of singular holomorphic distributions and their associated sheaves. We characterize either distributions whose tangent sheaf or conormal sheaf are arithmetically Cohen Macaulay (aCM) on \(X\). We also prove that a codimension one locally free distribution with trivial canonical bundle on any Fano threefold, with Picard number equal to one, has a tangent sheaf which either splits or it is stable.
MSC:
57R30 Foliations in differential topology; geometric theory
14J45 Fano varieties
14J60 Vector bundles on surfaces and higher-dimensional varieties, and their moduli
32S65 Singularities of holomorphic vector fields and foliations
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