Monodromy of Hypersurface Singularities

Invariant Subspaces of the Monodromy

We show that there are obstructions to the existence of certain types of invariant subspaces of the Milnor monodromy; this places restrictions on the cohomology of Milnor fibres of non-isolated hypersurface singularities.

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Strange duality and polar duality

We describe a relation between Arnold’s strange duality and a polar duality between the Newton polytopes which is mostly due to M. Kobayashi. We show that this relation continues to hold for the extension of Arnold’s strange duality found by C. T. C. Wall and the author. By a method of Ehlers-Varchenko, the characteristic polynomial of the monodromy of a hypersurface singularity can be computed...

Logarithmic Comparison Theorem versus Gauss–manin System for Isolated Singularities

For quasihomogeneous isolated hypersurface singularities, the logarithmic comparison theorem has been characterized explicitly by Holland and Mond. In the nonquasihomogeneous case, we give a necessary condition for the logarithmic comparison theorem in terms of the Gauss–Manin system of the singularity. It shows in particular that the logarithmic comparison theorem can hold for a nonquasihomoge...

A normal form algorithm for the Brieskorn lattice

Isolated hypersurface singularities form the simplest class of singularities. Their intensive study in the past has lead to a variety of invariants. The Milnor number is one of the simplest, and can easily be computed using standard basis methods. A finer invariant is the monodromy of the singularity. E. Brieskorn [Bri70] developed the theoretical background for computing the complex monodromy....