Homogeneous hypersurfaces in Kähler C-spaces with \(b_ 2=1\) (Q1824881)

A C-space Y in the author's terminology is a compact homogeneous Kähler space with \(b_ 2(Y)=1\). Examples are given by Hermitian compact symmetric spaces. In general, they are classified by pairs formed of a complex simple algebra and a simple positive root. The author characterizes the pairs (X,Y) of C-spaces such that X is a hypersurface in Y. The degree of the embedding is also given. There are five cases: Three standard cases (with quadrics and projective spaces), another series and an exceptional case. Some partial result in this direction was given by Y. Kimura. The main point in the proof is to determine when \(H^ q(\Omega^ 1_ Y(a))\) doesn't vanish.