Poincar\'e Series and Monodromy of the Simple and Unimodal Boundary Singularities

W. Ebeling

Trudy Matematicheskogo Instituta imeni V.A. Steklova, Singularities and applications, Tome 267 (2009), pp. 56-64.

Résumé

A boundary singularity is a singularity of a function on a manifold with boundary. The simple and unimodal boundary singularities were classified by V. I. Arnold and V. I. Matov. The McKay correspondence can be generalized to the simple boundary singularities. We consider the monodromy of the simple, parabolic, and exceptional unimodal boundary singularities. We show that the characteristic polynomial of the monodromy is related to the Poincaré series of the coordinate algebra of the ambient singularity.

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