  Let $f:\mathbb{C}^{n+1} \to \mathbb{C}$ be a germ of hypersurface with
isolated singularity. One can associate to $f$ a polarized variation of mixed
Hodge structure $\mathcal{H}$ over the punctured disc, where the Hodge
filtration is the limit Hodge filtration of W. Schmid and J. Steenbrink. By the
work of M. Saito and P. Deligne the VMHS associated to cohomologies of the
fibers of $f$ can be extended over the degenerate point $0$ of disc. The new
fiber obtained in this way is isomorphic to the module of relative
differentials of $f$ denoted $\Omega_f$. A mixed Hodge structure can be defined
on $\Omega_f$ in this way. The polarization on $\mathcal{H}$ deforms to
Grothendieck residue pairing modified by a varying sign on the Hodge graded
pieces in this process. This also proves the existence of a Riemann-Hodge
bilinear relation for Grothendieck pairing and allow to calculate the Hodge
signature of Grothendieck pairing.
