TY - JOUR

T1 - Orbifold zeta functions for dual invertible polynomials

AU - Ebeling, Wolfgang

AU - Gusein-Zade, Sabir M.

N1 - Funding information: This work was partly supported by DFG (Mercator fellowship, Grant Eb 102/8-1), Grants RFBR-16-01-00409 and NSh-2789.2016.1.

PY - 2017/2/1

Y1 - 2017/2/1

N2 - 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.

AB - 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.

KW - Group action

KW - Invertible polynomial

KW - Monodromy

KW - Orbifold zeta function

UR - http://www.scopus.com/inward/record.url?scp=84969884797&partnerID=8YFLogxK

UR - https://arxiv.org/abs/1407.0154

U2 - 10.1017/S0013091516000043

DO - 10.1017/S0013091516000043

M3 - Article

AN - SCOPUS:84969884797

VL - 60

SP - 99

EP - 106

JO - Proceedings of the Edinburgh Mathematical Society

JF - Proceedings of the Edinburgh Mathematical Society

SN - 0013-0915

IS - 1

ER -