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Logarithmic comparison theorem versus Gauss–Manin system for isolated singularities
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Mathias Schulze
Published/Copyright:
April 13, 2010
Abstract
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 nonquasihomogeneous singularity only if 1 is an eigenvalue of the monodromy.
Received: 2008-06-01
Revised: 2008-07-09
Published Online: 2010-04-13
Published in Print: 2010-October
© de Gruyter 2010
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Articles in the same Issue
- A combinatorial approach to Alexander–Hirschowitz's Theorem based on toric degenerations
- Triply periodic minimal surfaces which converge to the Hoffman–Wohlgemuth example
- Total absolute horospherical curvature of submanifolds in hyperbolic space
- The case of equality for an inverse Santaló functional inequality
- Circle configurations in strictly convex normed planes
- Rank four vector bundles without theta divisor over a curve of genus two
- Affine Tallini Sets and Grassmannians
- Geometry of self-dual flats over a PID on a polarity
- Logarithmic comparison theorem versus Gauss–Manin system for isolated singularities
- A kinematic formula for the total absolute curvature of intersections
- Reducible Veronese surfaces
- Effective non-vanishing conjectures for projective threefolds
