3 M ay 2 00 1 Abelian simply transitive affine groups of symplectic type
نویسندگان
چکیده
We construct a model space C(sp(R 2n)) for the variety of Abelian simply transitive groups of affine transformations of type Sp(R 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 R 2n. 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(sp(R 2n)).
منابع مشابه
Abelian simply transitive affine groups of symplectic type Oliver
The set of all Abelian simply transitive subgroups of the affine group naturally corresponds to the set of real solutions of a system of algebraic equations. We classify all simply transitive subgroups of the symplectic affine group by constructing a model space for the corresponding variety of solutions. Similarly, we classify the complete global model spaces for flat special Kähler manifolds ...
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