Deformation of rational singularities and Hodge structure

For a one-parameter degeneration of reduced compact complex analytic spaces dimension $n$, we prove the invariance frontier Hodge numbers $h^{p,q}$ (that is, with $pq(n-p)(n-q)=0$) for intersection cohomology fibers and also their desingularizations, assuming that central fiber is reduced, projective, has only rational singularities. This can be shown to equivalent structure sheaf (which known in algebraizable case), since symmetry all together $E_1$-degeneration Hodge-to-de Rham spectral sequence nearby fibers, projectivity fiber. For proof main theorem, calculate certain graded pieces induced $V$-filtration first non-zero member filtration on module total space, which coincides direct image dualizing desingularization as Kollar's conjecture. calculation implies order nilpotence local monodromy smaller than general singularity case by 2 situation theorem further smoothness fibers. We partial converse under some hypothesis.