Quasihomogene isolierte Singularit�ten von Hyperfl�chen

Period mapping via Brieskorn modules

“…[22]. (This argument is same as [22, 4.3] where we proved that the primitive form is an eigenvector of E.) In particular, if /o is not quasihomogeneous, we have Ao(0) / 0 (using [32]), and E' is not zero at 0 e A x S' by (3.1.3), (3.6.6). We can also verify directly (3.5.2) in the example /o = x p -{-y Q -^z r -\-xyz with l/j?+ 1/q + 1/r < 1.…”

Linear free divisors and the global logarithmic comparison theorem

“…As the germ of a curve, (D , p ) has an isolated singularity. Then (D , p ), and hence (D, p), are quasihomogeneous, by Saito's theorem [21]. For n = 4 analogous arguments yield S 0 = T 0 = {0} and S 2 = T 2 .…”

Logarithmic cohomology of the complement of a plane curve

“…Our proof shows that if h is a local equation of D, and the logarithmic comparison theorem holds, then there is a vector field germ χ such that χ · h = h. As a reduced curve has isolated singularities, we can then apply the theorem of K. Saito [10]: if h ∈ O C n ,0 has isolated singularity and h belongs to its Jacobian ideal J h then in suitable coordinates h is weighted homogeneous.…”