Graded Koszul cohomology and spectrum of certain homogeneous polynomials
Résumé
Using the graded duality of the cohomology of the Koszul complexes defined by the partial derivatives of homogeneous polynomials with one-dimensional singular loci, we get some formulas for their Poincare series generalizing a well-known result in the isolated singularity case. We also show some relations with the spectrum in the sense of Steenbrink by introducing the pole order spectrum and using the pole order spectral sequence as well as the Gauss-Manin systems and the Brieskorn modules in a generalized sense.