A classification of weighted homogeneous Saito free divisors
The purpose of the paper is to obtain a complete list of weighted homogeneous Saito free divisors in the three-dimensional affine space over \(\mathbb C\). The approach is mainly based on properties of Lie algebras of vector fields tangent to reduced hypersurfaces at their non-singular points. A complete list of such Lie algebras consists of 17 weighted homogeneous polynomials. This set is naturally subdivided in three subsets containing 2, 7 and 8 elements related with discriminants of irreducible real reflection groups of type \(A_3,\) \(B_3\) and \(H_3,\) respectively. Then, some interesting relationships between 17 polynomials and root systems of types \(E_{6}, E_{7}\) and \(E_{8}\) as well as few examples in higher dimensional cases are briefly discussed. In fact, the computational part of the work is a strong simplification of earlier results from [in: Algebraic analysis and number theory, RIMS Kôkyûroku 810, 85--94 (1992; Zbl 0966.17500)].
scientific article; zbMATH DE number 5651144
scientific article