In the study of holomorphic distributions and foliations in complex projective manifolds
X; algebro-geometric techniques have been used.
A Fano variety is a projective manifold X such that the anticanonical line bundle
is ample. In my Phd thesis, we studied holomorphic distributions of dimension and codi-
mension one on smooth weighted projective complete intersection Fano threedimensional
manifolds, with Picard number equal to one.
The goal of this work is to characterize this distributions whose tangent sheaf and conor-
mal sheaf are arithmetically Cohen Macaulay (aCM), i.e. has no intermediate cohomology.
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.
This a joint work with Mauricio Corrêa and Simone Marchesi.
