Basalaev, Alexey; Takahashi, Atsushi; Werner, Elisabeth Orbifold Jacobian algebras for exceptional unimodal singularities. (English) Zbl 1393.14003 Arnold Math. J. 3, No. 4, 483-498 (2017). Let \(f\) be an invertible polynomial defining an exceptional unimodal singularity from the list of V. I. Arnol’d [Russ. Math. Surv. 30, No. 5, 1–75 (1975; Zbl 0343.58001)]. The authors show that the orbifold Jacobian algebra of \(f\) (see [A. Basalaev et al., “Orbifold Jacobian algebras for invertible polynomials”, Preprint, arXiv:1608.08962]) is isomorphic to the ordinary Jacobian algebra of the Berglund-Hübsch transpose of another invertible polynomial (see [P. Berglund and T. Hübsch, Nucl. Phys., B 393, No. 1–2, 377–391 (1993; Zbl 1245.14039)]), which determines the strange dual singularity in the sense of Arnold (cf. also [W. Ebeling and A. Takahashi, Arnold Math. J. 2, No. 3, 277–298 (2016; Zbl 1357.14054)]). Reviewer: Aleksandr G. Aleksandrov (Moskva) Cited in 12 Documents MSC: 14B05 Singularities in algebraic geometry 58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces 57R45 Singularities of differentiable mappings in differential topology Keywords:singularity theory; hypersurface singularities; exceptional unimodal singularities; Jacobian algebras; invertible polynomials; Arnold’s strange duality; Berglund-Hübsch transform; mirror symmetry Citations:Zbl 0343.58001; Zbl 1245.14039; Zbl 1357.14054 PDFBibTeX XMLCite \textit{A. Basalaev} et al., Arnold Math. J. 3, No. 4, 483--498 (2017; Zbl 1393.14003) Full Text: DOI arXiv References: [1] Arnold, V.I., Gusein-Zade, S., Varchenko, A.: Singularities of Differentiable Maps, vol. 2. Birkhäuser, Boston (2012) · Zbl 1290.58001 · doi:10.1007/978-0-8176-8340-5 [2] Basalaev, A., Takahashi, A., Werner, E.: Orbifold Jacobian algebras for invertible polynomials. arXiv:1608.08962 · Zbl 1393.14003 [3] Carqueville, N., Ros Camacho, A., Runkel, I.: Orbifold equivalent potentials. J. Pure Appl. Algebra 220(2), 759-781 (2016) · Zbl 1333.18004 · doi:10.1016/j.jpaa.2015.07.015 [4] Ebeling, W., Takahashi, A.: Strange duality of weighted homogeneous polynomials. Compos. Math. 147(5), 1413-33 (2011) · Zbl 1238.14029 · doi:10.1112/S0010437X11005288 [5] Ebeling, W., Takahashi, A.: Variance of the exponents of orbifold Landau-Ginzburg models. Math. Res. Lett. 20(1), 51-65 (2013) · Zbl 1285.32012 · doi:10.4310/MRL.2013.v20.n1.a5 [6] Kawai, T., Yang, S.-K.: Duality of orbifoldized elliptic genera. Progr. Theoret. Phys. Suppl. 118, 277-297 (1995) · Zbl 0874.14040 · doi:10.1143/PTPS.118.277 [7] Krawitz, M., Priddis, N., Acosta, P., Bergin, N., Rathnakumara, H.: FJRW-rings and mirror symmetry. Commun. Math. Phys. 296(1), 145-174 (2010) · Zbl 1250.81087 · doi:10.1007/s00220-009-0929-7 [8] Newton, R., Ros Camacho, A.: Strangely dual orbifold equivalence I. J. Singul. 14, 34-51 (2016) · Zbl 1375.14014 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.