On the structure of Brieskorn lattice

the filtration F on Ox' The right hand side of (*) was first studied J f by Brieskorn [B] and we call it the Brieskorn lattice of M, and denote it by Mo. In fact, he defined the regular singular connection (called the Gauss-Manin connection) on Mo, which calculates the Milnor monodromy. We can easily verify that the connection V is compatible with the action of 9f on M as left Z>s,o-module, where t is the coordinate of S'. More precisely, the inverse of the action of Va/^resp.c^) is well-defined as a C-endomorphism of Mo(resp.M) and they coincide on F-nM by the isomorphism (*)

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