Cusp singularities and quasi-polyhedral sets

descriptionPublicationkeyboard_double_arrow_right Article , Other literature type 07 Mar 2019Publisher:Mathematical Society of JapanJournal:Advanced Studies in Pure Mathematics (issn: 0920-1971,

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Authors: Ishida, Masanori;

doi: 10.2969/aspm/07510163

Cusp singularities and quasi-polyhedral sets

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Abstract

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.

Keywords

cusp singularity, Toric variety, lattice polytope, 52B20, 20F55, 14M25, reflection group

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