Parametric local cohomology classes and Tjurina stratifications for μ-constant deformations of quasi-homogeneous singularities

摘要

Local cohomology classes attached to semi-quasihomogeneous hypersurface isolated singularities are considered. A new effective method to compute Tjurina stratifications associated with μ-constant deformation f_t(x) = F(x,t), t ∈ T of weighted homogeneous isolated singularities is proposed. The proposed method also computes on each stratum, via Grothendieck local duality, a parametric standard basis of the relevant ideal quotient J_t : f_t, where J_t stands for the Jacobi ideal of the function f_t in the local ring of germs of holomorphic functions. The key idea in this approach is the use of parametric local cohomology classes.