-adic Teichmüller space and Siegel halfspace
Every compact Kähler surface is deformation equivalent to a projective surface. In particular, topologically Kähler surfaces and projective surfaces cannot be distinguished. Kodaira had asked whether this continues to hold in higher dimensions. We explain the construction of a series of counter-examples due to C. Voisin, which yields compact Kähler manifolds of dimension at least four whose rational homotopy type is not realized by any projective manifold.
The degenerate Cauchy problem in a Banach space is studied on the basis of properties of an abstract analytical function, satisfying the Hilbert identity, and a related pair of operators A, B.