Jacobian rings and the infinitesimal Torelli Theorem

Abstract: In this article we deal with jacobian rings and identify a mixed Hodge component of a nondegenerate hypersurface in the torus with a lattice geometric quotient vector space. We introduce a period map, study its differential and compute the kernel of the differential much explicitly via certain Laurent polynomials. As an application we deal with the infinitesimal Torelli theorem.