and
Type II supergravity is a supergravity in dimension 10 which is the low-energy effective quantum field theory underlying type II string theory.
See the general references at supergravity.
A relation of the U-duality symmetry to generalized complex geometry is discussed in
André Coimbra, Charles Strickland-Constable, Daniel Waldram, Supergravity as Generalised Geometry I: Type II Theories (arXiv:1107.1733)
Paulo Pires Pacheco, Daniel Waldram, M-theory, exceptional generalised geometry and superpotentials (arXiv:0804.1362)
A thesis reviewing some aspects is