The aim of the paper under review is to describe the algebraic varieties for simply transitive Abelian affine groups of symplectic type. Special Kaehler manifolds arise from holomorphic potentials (locally). The flat case corresponds to those holomorphic potentials satisfying some algebraic conditions on the third derivatives. This condition can be interpreted as an associativity condition on an associated bilinear product on the tangent spaces of a special Kaehler manifold. In the non-definite case, the algebraic constraint on cubic tensors generates a non-trivial variety of solutions. This allows the authors to classify locally flat special Kaehler manifolds with constant cubic form. In particular, the points of the above variety correspond to some complete simply connected global models of such manifolds. These spaces are complete in both senses (with respect to the metric connection and the affine connection). All of them arise from some Abelian transitive affine groups of symplectic type.