 The Hodge numbers of "Xb" are the same as those of "X"0, so the number is independent of "b".The period map is the map
where "F" is the flag variety of chains of subspaces of dimensions "b""p","k" for all "p", that sends

Because "Xb" is a Kähler manifold, the Hodge filtration satisfies the Hodge–Riemann bilinear relations.These imply that
Not all flags of subspaces satisfy this condition.