  We construct a model space $C(\gsp(\bR^{2n}))$ for the variety of Abelian
simply transitive groups of affine transformations of type ${\rm
Sp}(\bR^{2n})$. The model is stratified and its principal stratum is a
Zariski-open subbundle of a natural vector bundle over the Grassmannian of
Lagrangian subspaces in $\bR^{2n}$. \noindent Next we show that every flat
special K\"ahler manifold may be constructed locally from a holomorphic
function whose third derivatives satisfy some algebraic constraint. In
particular global models for flat special K\"ahler manifolds with constant
cubic form correspond to a subvariety of $C(\gsp(\bR^{2n}))$.
