Logarithmic comparison theorem versus Gauss-Manin system for isolated singularities

Details Logarithmic comparison theorem versus Gauss-Manin system for isolated singularities Logarithmic comparison theorem versus Gauss-Manin system for isolated singularities

2007-06-17

arxiv.org/abs/0706.2512v2

Adv. Geom. 10,4 (2010), 699-708

Mathematics

Algebraic Geometry

9 pages

Scientific paper

10.1515/ADVGEOM.2010.023

For quasihomogeneous isolated hypersurface singularities, the logarithmic comparison theorem has been characterized explicitly by Holland and Mond. In the non quasihomogeneous 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 non quasihomogeneous singularity only if 1 is an eigenvalue of the monodromy.

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