On supersymmetric solutions of type IIB supergravity with general fluxes

We propose a general spinor ansatz to find supersymmetric configurations preserving 4-dimensional Poincaré invariance in the context of type IIB supergravity in the presence of general fluxes. We show how this removes the imaginary-selfduality (ISD) constraint on the 3-form flux and present a simple example with non-vanishing (1,2)+(0,3) flux. To characterize the geometrical properties of such configurations we will use the tool of SU(2) structures on the internal space, which are naturally linked to the form of the ansatz we propose.