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Abelian simply transitive affine groups of symplectic type

Oliver Baues·Vicente Cortes
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Abstract

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 Kähler manifold may be constructed locally from a holomorphic function whose third derivatives satisfy some algebraic constraint. In particular global models for flat special Kähler manifolds with constant cubic form correspond to a subvariety of $C(\gsp(\bR^{2n}))$.

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Oliver Baues, Vicente Cortes. 2002-11-28. Abelian simply transitive affine groups of symplectic type. https://arxiv.org/abs/math/0105025

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