Details
Original language | English |
---|---|
Article number | 051 |
Pages (from-to) | 1-15 |
Number of pages | 15 |
Journal | SIGMA |
Volume | 16 |
Issue number | 51 |
Publication status | Published - 11 Jun 2020 |
Abstract
Keywords
- Berglund–Hübsch–Henningson–Takahashi duality, Group action, Invertible polynomial, Mirror symmetry, Orbifold Euler characteristic
ASJC Scopus subject areas
- Mathematics(all)
- Analysis
- Mathematics(all)
- Mathematical Physics
- Mathematics(all)
- Geometry and Topology
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In: SIGMA, Vol. 16, No. 51, 051, 11.06.2020, p. 1-15.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Dual Invertible Polynomials with Permutation Symmetries and the Orbifold Euler Characteristic
AU - Ebeling, Wolfgang
AU - Gusein-Zade, Sabir M.
N1 - Funding information: This work was partially supported by DFG. The work of the second author (Sections 2 and 4) was supported by the grant 16-11-10018 of the Russian Foundation for Basic Research. We are very grateful to the referees of the paper for their useful comments.
PY - 2020/6/11
Y1 - 2020/6/11
N2 - P. Berglund, T. Hübsch, and M. Henningson proposed a method to construct mirror symmetric Calabi–Yau manifolds. They considered a pair consisting of an invertible polynomial and of a finite (abelian) group of its diagonal symmetries together with a dual pair. A. Takahashi suggested a method to generalize this construction to symmetry groups generated by some diagonal symmetries and some permutations of variables. In a previous paper, we explained that this construction should work only under a special condition on the permutation group called parity condition (PC). Here we prove that, if the permutation group is cyclic and satisfies PC, then the reduced orbifold Euler characteristics of the Milnor fibres of dual pairs coincide up to sign.
AB - P. Berglund, T. Hübsch, and M. Henningson proposed a method to construct mirror symmetric Calabi–Yau manifolds. They considered a pair consisting of an invertible polynomial and of a finite (abelian) group of its diagonal symmetries together with a dual pair. A. Takahashi suggested a method to generalize this construction to symmetry groups generated by some diagonal symmetries and some permutations of variables. In a previous paper, we explained that this construction should work only under a special condition on the permutation group called parity condition (PC). Here we prove that, if the permutation group is cyclic and satisfies PC, then the reduced orbifold Euler characteristics of the Milnor fibres of dual pairs coincide up to sign.
KW - Berglund–Hübsch–Henningson–Takahashi duality
KW - Group action
KW - Invertible polynomial
KW - Mirror symmetry
KW - Orbifold Euler characteristic
UR - http://www.scopus.com/inward/record.url?scp=85089703521&partnerID=8YFLogxK
U2 - 10.3842/SIGMA.2020.051
DO - 10.3842/SIGMA.2020.051
M3 - Article
VL - 16
SP - 1
EP - 15
JO - SIGMA
JF - SIGMA
IS - 51
M1 - 051
ER -