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Orbifold Zeta Functions for Dual Invertible Polynomials

Published online by Cambridge University Press:  23 May 2016

Wolfgang Ebeling
Affiliation:
Leibniz Universität Hannover, Institut für Algebraische Geometrie, Postfach 6009, 30060 Hannover, Germany (ebeling@math.uni-hannover.de)
Sabir M. Gusein-Zade
Affiliation:
Moscow State University, Faculty of Mechanics and Mathematics, Moscow, GSP-1, 119991, Russia (sabir@mccme.ru)

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.

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 2016 

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