The moduli space of Kähler structures on a real compact symplectic manifold (Q1109185)

Let (M,\(\omega)\) be a compact symplectic \(C^{\infty}\)-manifold. The authors construct and study the moduli space of all complex structures on M for which \(\omega\) is a Kähler form. This moduli space is in general infinite dimensional. Its geometry is described in terms of the category of manifolds modelled on inverse limits of Hilbert spaces as developed by \textit{H. Omori}, ''Infinite dimensional Lie transformation groups'' (1974; Zbl 0328.58005).