  Let f : Y -> X be a morphism of complex projective manifolds, and let F be a
subsheaf of the tangent bundle which is closed under the Lie bracket, but not
necessarily a foliation. This short paper contains an elementary and very
geometric argument to show that all obstructions to deforming the morphism f
along the sheaf F lie in the first cohomology group H^1(Y, F_Y) of the sheaf
F_Y, which is the image of f^*(F) in f^*(T_X) under the pull-back of the
inclusion map.
  Special cases of this result include the theory of deformation along a
(possibly singular) foliation, logarithmic deformation theory and deformations
with fixed points.
