The Definitions of Special Geometry
  The scalars in vector multiplets of N=2 supersymmetric theories in 4 dimensions exhibit `special Kaehler geometry', related to duality symmetries, due to their coupling to the vectors. In the literature there is some confusion on the definition of special geometry, which we want to clear up, for rigid as well as for local N=2. 
Ben Craps, Frederik Roose, Walter Troost and Antoine Van Proeyen,   (K.U. Leuven)