Mirror map for Fermat polynomials with a~nonabelian group of
Teoretičeskaâ i matematičeskaâ fizika, Tome 209 (2021) no. 2, pp. 205-223
Voir la notice de l'article provenant de la source Math-Net.Ru
We study Landau–Ginzburg orbifolds $(f,G)$ with $f=x_1^n+\cdots+x_N^n$ and $G=S\ltimes G^d$, where $S\subseteq S_N$ and $G^d$ is either the maximal group of scalar symmetries of $f$ or the intersection of the maximal diagonal symmetries of $f$ with $SL_N(\mathbb{C})$. We construct a mirror map between the corresponding phase spaces and prove that it is an isomorphism restricted to a certain subspace of the phase space when $n=N$ is a prime number. When $S$ satisfies the parity condition of Ebeling–Gusein-Zade, this subspace coincides with the full space. We also show that two phase spaces are isomorphic for $n=N=5$.
Keywords:
mirror symmetry, nonabelian symmetry group, singularity theory.
@article{TMF_2021_209_2_a0,
author = {A. A. Basalaev and A. A. Ionov},
title = {Mirror map for {Fermat} polynomials with a~nonabelian group of},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {205--223},
publisher = {mathdoc},
volume = {209},
number = {2},
year = {2021},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2021_209_2_a0/}
}
TY - JOUR AU - A. A. Basalaev AU - A. A. Ionov TI - Mirror map for Fermat polynomials with a~nonabelian group of JO - Teoretičeskaâ i matematičeskaâ fizika PY - 2021 SP - 205 EP - 223 VL - 209 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TMF_2021_209_2_a0/ LA - ru ID - TMF_2021_209_2_a0 ER -
A. A. Basalaev; A. A. Ionov. Mirror map for Fermat polynomials with a~nonabelian group of. Teoretičeskaâ i matematičeskaâ fizika, Tome 209 (2021) no. 2, pp. 205-223. http://geodesic.mathdoc.fr/item/TMF_2021_209_2_a0/