The Jacobian module, the Milnor fiber, and the \(D\)-module generated by \(f^s\) (Q517432)

The author considers a function germ \(f\) on a complex manifold \(X\) and constructs a Liouville complex, coming from the action of a Liouville form on the logarithmic differential forms associated to \(f\). He uses this complex to relate the D-module generated by \(f^s\) to the Jacobian ideal of \(f\), which in turn is related to the cohomology of the Milnor fiber of \(f\). Several important results on hyperplane arrangements are also included: a proof of Terao's conjecture on the annihilator of \(1/f\) and its relations with the Strong Monodromy Conjecture.