Special geometry without special coordinates

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Abstract
Presents a detailed geometric derivation of N=2, 4D supergravity coupled to Abelian vector multiplets (1,1/2,0). The theory is covariant under reparametrisations of the manifold M spanned by the scalar fields. By requiring the closure of the supersymmetry transformation laws, the authors find a coordinate-free characterisation of M. The geometry of M, called 'special geometry', is relevant to compactified string theories, since it is common to the moduli spaces of Calabi-Yau threefolds and c=9 (2,2) superconformal field theories.