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Orbifold Zeta Functions for Dual Invertible Polynomials

Part of: Affine geometry Surfaces and higher-dimensional varieties Differential topology Theory of singularities and catastrophe theory

Published online by Cambridge University Press:  23 May 2016

Wolfgang Ebeling  and
Sabir M. Gusein-Zade
Wolfgang Ebeling
Affiliation:
Leibniz Universität Hannover, Institut für Algebraische Geometrie, Postfach 6009, 30060 Hannover, Germany ([email protected])
Sabir M. Gusein-Zade
Affiliation:
Moscow State University, Faculty of Mechanics and Mathematics, Moscow, GSP-1, 119991, Russia ([email protected])
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Abstract

An invertible polynomial in n variables is a quasi-homogeneous polynomial consisting of n monomials so that the weights of the variables and the quasi-degree are well defined. In the framework of the construction of mirror symmetric orbifold Landau–Ginzburg models, Berglund, Hübsch and Henningson considered a pair (f, G) consisting of an invertible polynomial f and an abelian group G of its symmetries together with a dual pair . Here we study the reduced orbifold zeta functions of dual pairs (f, G) and and show that they either coincide or are inverse to each other depending on the number n of variables.

Keywords

invertible polynomialgroup actionmonodromyorbifold zeta function

MSC classification

Secondary: 14J33: Mirror symmetry 14R20: Group actions on affine varieties 57R18: Topology and geometry of orbifolds 58K10: Monodromy
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 60 , Issue 1 , February 2017 , pp. 99 - 106
Copyright
Copyright © Edinburgh Mathematical Society 2016 

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