A generalization of Griffiths's theorem on rational integrals

Abstract

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])