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We use the formalism of generalized geometry to study the genericsupersymmetric AdS_5 solutions of type IIB supergravity that are dual to N=1superconformal field theories (SCFTs) in d=4. Such solutions have an associatedsix-dimensional generalized complex cone geometry that is an extension ofCalabi-Yau cone geometry. We identify generalized vector fields dual to thedilatation and R-symmetry of the dual SCFT and show that they are generalizedholomorphic on the cone. We carry out a generalized reduction of the cone to atransverse four-dimensional space and show that this is also a generalizedcomplex geometry, which is an extension of Kahler-Einstein geometry.Remarkably, provided the five-form flux is non-vanishing, the cone issymplectic. The symplectic structure can be used to obtain Duistermaat-Heckmantype integrals for the central charge of the dual SCFT and the conformaldimensions of operators dual to BPS wrapped D3-branes. We illustrate theseresults using the Pilch-Warner solution.

AdS_5 Solutions of Type IIB Supergravity and Generalized Complex Geometry