We generalize Griffiths's theorem on the Hodge filtration of the primitive cohomology of a smooth projective hypersurface using the local Bernstein-Sato polynomials, the $V$ -filtration of Kashiwara [22] and Malgrange [27] along the hypersurface, and the Brieskorn module of the global defining equation of the hypersurface (see [4])
@article{1161093266,
author = {Dimca, Alexandru and Saito, Morihiko},
title = {A generalization of Griffiths's theorem on rational integrals},
journal = {Duke Math. J.},
volume = {131},
number = {1},
year = {2006},
pages = { 303-326},
language = {en},
url = {http://dml.mathdoc.fr/item/1161093266}
}
Dimca, Alexandru; Saito, Morihiko. A generalization of Griffiths's theorem on rational integrals. Duke Math. J., Tome 131 (2006) no. 1, pp. 303-326. http://gdmltest.u-ga.fr/item/1161093266/