Hypersurfaces of the Flag Variety: Deformation theory and the Theorems of Kodaira-Spencer, Torelli, Lefschetz, M. Noether and Serre.
In this brief note we give a proof that a certain family of Fano 4-folds, described below, is complex (locally) complete and effectively parametrized in the sense of Kodaira-Spencer [Ko-Sp].