  We use the formalism of generalized geometry to study the generic
supersymmetric AdS_5 solutions of type IIB supergravity that are dual to N=1
superconformal field theories (SCFTs) in d=4. Such solutions have an associated
six-dimensional generalized complex cone geometry that is an extension of
Calabi-Yau cone geometry. We identify generalized vector fields dual to the
dilatation and R-symmetry of the dual SCFT and show that they are generalized
holomorphic on the cone. We carry out a generalized reduction of the cone to a
transverse four-dimensional space and show that this is also a generalized
complex geometry, which is an extension of Kahler-Einstein geometry.
Remarkably, provided the five-form flux is non-vanishing, the cone is
symplectic. The symplectic structure can be used to obtain Duistermaat-Heckman
type integrals for the central charge of the dual SCFT and the conformal
dimensions of operators dual to BPS wrapped D3-branes. We illustrate these
results using the Pilch-Warner solution.
