A geometric construction of Coxeter-Dynkin diagrams of bimodal singularities

Details A geometric construction of Coxeter-Dynkin diagrams of bimodal singularities A geometric construction of Coxeter-Dynkin diagrams of bimodal singularities

2011-02-24

arxiv.org/abs/1102.5024v1

Mathematics

Algebraic Geometry

18 pages, 8 figures

Scientific paper

We consider the Berglund-H\"ubsch transpose of a bimodal invertible polynomial and construct a triangulated category associated to the compactification of a suitable deformation of the singularity. This is done in such a way that the corresponding Grothendieck group with the (negative) Euler form can be described by a graph which corresponds to the Coxeter-Dynkin diagram with respect to a distinguished basis of vanishing cycles of the bimodal singularity.

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