Deformation along subsheaves, II

  • Clemens Jörder

    Universität Freiburg, Germany
  • Stefan Kebekus

    Universität Freiburg, Germany
Deformation along subsheaves, II cover

A subscription is required to access this book chapter.


Let be the inclusion map of a compact reduced subspace of a complex manifold, and let be a subsheaf of the tangent bundle which is closed under the Lie bracket, but not necessarily a sheaf of -algebras. This paper discusses criteria to guarantee that infinitesimal deformations of which are induced by lift to positive-dimensional deformations of , where is deformed “along the sheaf ”.

In case where is complex-symplectic and the sheaf of locally Hamiltonian vector fields, this partially reproduces known results on unobstructedness of deformations of Lagrangian submanifolds. 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.