  Let Y be a compact reduced subspace of a complex manifold X, and let F be a
subsheaf of the tangent bundle T_X which is closed under the Lie bracket. This
paper discusses criteria to guarantee that infinitesimal deformations of the
inclusion morphism Y -> X give rise to positive-dimensional deformation
families, deforming the inclusion map "along the sheaf F". In case where X is
complex-symplectic and F is the sheaf of Hamiltonian vector fields, this
partially reproduces known results on unobstructedness of deformations of
Lagrangian submanifolds.
  Written for the IMPANGA Lecture Notes series, this paper aims at simplicity
and clarity of argument. It does not strive to present the shortest proofs or
most general results available. The proof is rather elementary and geometric,
constructing higher-order liftings of a given infinitesimal deformation using
flow maps of carefully crafted time-dependent vector fields.
