Abelian simply transitive affine groups of symplectic type

Details Abelian simply transitive affine groups of symplectic type Abelian simply transitive affine groups of symplectic type

2001-05-03

arxiv.org/abs/math/0105025v2

Annales Inst.Fourier 52 (2002) 1729-1751

Mathematics

Differential Geometry

corrected typos, updated references

Scientific paper

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 $C(\gsp(\bR^{2n}))$.

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