Infinitesimal Torelli theorem for complete intersections in certain homogeneous Kähler manifolds
The result proved in this paper is a generalization of the theorem of Peters and Usui that the infinitesimal Torelli theorem holds for any nonsingular complete intersection with ample canonical bundle in a projective space. Let Y be a compact, simply-connected, homogeneous Kähler manifold whose second Betti number is one. The author shows that if X is a nonsingular complete intersection in Y with ample canonical bundle then the infinitesimal Torelli theorem holds for X, provided that at least one of several conditions on X and Y is satisfied. For example, it is enough to assume that Y is an irreducible Hermitian symmetric space of compact type. It is hoped that the proof can be modified to apply when these conditions are omitted.
scientific article; zbMATH DE number 4019206