[For the entire collection see Zbl 0528.00004.]
The following statement if referred to as generic global Torelli theorem: Let 01M be a moduli space for algebraic manifolds \(X_ s\), \(s\in {\mathcal M}\), and let \(\phi: {\mathcal M}\to \Gamma \setminus D\) be a period map. Then \(\phi\) is a degree one map onto its image. This theorem holds true if for a general s the infinitesimal variation of Hodge structures uniquely determines \(X_ s\). The proofs of two results are outlined: (A) The generic global Torelli theorem holds true for smooth cubic hypersurfaces in \(P^{3m+1}\). But there is a better result by R. Donagi in chapter XIII of the same book [”Generic Torelli and variational Schottky”, ibid. 239-258 (1984)]. (B) The Fermat surface in \(P_ 3\) of degree \(d\geq 5\) is uniquely determined by its infinitesimal variation of Hodge structures.