Advanced Studies in Pure Mathematics

Cusp singularities and quasi-polyhedral sets

Masanori Ishida

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We study cusp singularities from the viewpoint of locally polyhedral sets and reflection groups. Following the definition of quasi-polyhedral sets by Grünbaum, we consider a special kind of rational quasi-polyhedral sets with group action and refer to the relation with cusp singularities. We give also some examples of such quasi-polyhedral sets by using discrete groups generated by reflections.

Article information

Algebraic Varieties and Automorphism Groups, K. Masuda, T. Kishimoto, H. Kojima, M. Miyanishi and M. Zaidenberg, eds. (Tokyo: Mathematical Society of Japan, 2017), 163-182

Received: 8 April 2015
Revised: 25 September 2015
First available in Project Euclid: 21 September 2018

Permanent link to this document euclid.aspm/1537498708

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14M25: Toric varieties, Newton polyhedra [See also 52B20]
Secondary: 52B20: Lattice polytopes (including relations with commutative algebra and algebraic geometry) [See also 06A11, 13F20, 13Hxx] 20F55: Reflection and Coxeter groups [See also 22E40, 51F15]

Toric variety cusp singularity lattice polytope reflection group


Ishida, Masanori. Cusp singularities and quasi-polyhedral sets. Algebraic Varieties and Automorphism Groups, 163--182, Mathematical Society of Japan, Tokyo, Japan, 2017. doi:10.2969/aspm/07510163.

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