On the structure of Brieskorn lattice

Period mapping via Brieskorn modules

“…[22]. (This argument is same as [22, 4.3] where we proved that the primitive form is an eigenvector of E.) In particular, if /o is not quasihomogeneous, we have Ao(0) / 0 (using [32]), and E' is not zero at 0 e A x S' by (3.1.3), (3.6.6).…”

“…It follows from the uniqueness of MALGRANGE'S extension [31]. In fact, a good basis at the origin is uniquely extended to a good basis at s G S by fixing an opposite filtration in [22] and using the parallel translation of the splitting of the Hodge filtration in [loc. cit.}…”

“…-Let v = t {v\.,..., v^) be a good basis of the Brieskorn module 7^ in [22]. Let /' be a miniversal deformation of /o as in (3.1), and S' its base space.…”

“…-Using MALGRANGE'S extension [31] of a good basis in [22] (cf. also (3.6)), it is possible to get a correct version of THEOREM in [8, (5. It is also well known that :…”

“…(3.4), using the structure of Brieskorn module [22], because the Hodge filtration of the vanishing cohomology is obtained by the graduation of the Brieskorn module by the filtration V, cf. (2.6.1), where the information lost by the graduation is expressed by the linear mappings c^ in [loc.…”