Journal of the Mathematical Society of Japan
- J. Math. Soc. Japan
- Volume 61, Number 4 (2009), 1071-1095.
A classification of weighted homogeneous Saito free divisors
We describe an approach to classification of weighted homogeneous Saito free divisors in . This approach is mainly based on properties of Lie algebras of vector fields tangent to reduced hypersurfaces at their non-singular points. In fact we also obtain a classification of such Lie algebras having similar properties as ones for discriminants associated with irreducible real reflection groups of rank 3. Among other things we briefly discuss some applications to the theory of discriminants of irreducible reflection groups of rank 3, some interesting relationships with root systems of types , , , and few examples in higher dimensional cases.
J. Math. Soc. Japan, Volume 61, Number 4 (2009), 1071-1095.
First available in Project Euclid: 6 November 2009
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 14B05: Singularities [See also 14E15, 14H20, 14J17, 32Sxx, 58Kxx]
Secondary: 14J17: Singularities [See also 14B05, 14E15] 32S26 32S65: Singularities of holomorphic vector fields and foliations
SEKIGUCHI, Jiro. A classification of weighted homogeneous Saito free divisors. J. Math. Soc. Japan 61 (2009), no. 4, 1071--1095. doi:10.2969/jmsj/06141071. https://projecteuclid.org/euclid.jmsj/1257520500