Journal of the Mathematical Society of Japan

A classification of weighted homogeneous Saito free divisors


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We describe an approach to classification of weighted homogeneous Saito free divisors in $\mbi{C}^{3}$. 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 $E_{6}$, $E_{7}$, $E_{8}$, and few examples in higher dimensional cases.

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J. Math. Soc. Japan Volume 61, Number 4 (2009), 1071-1095.

First available in Project Euclid: 6 November 2009

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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

logarithmic vector fields discriminants non-isolated singularities Coxeter groups Lie algebras


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.

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