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An example of Berglund-Hübsch mirror symmetry for a Calabi-Yau complete intersection. (English) Zbl 1402.14051

Summary: We study an example of complete intersection Calabi-Yau threefold due to A. Libgober and J. Teitelbaum [Int. Math. Res. Not. 1993, No. 1, 29–39 (1993; Zbl 0789.14005)], and verify mirror symmetry at a cohomological level. Direct computations allow us to propose an analogue to the P. Berglund and T. Hübsch mirror symmetry setup for this example [Nucl. Phys., B 393, No. 1–2, 377–391 (1993; Zbl 1245.14039)]. We then follow the approach of M. Krawitz to propose an explicit mirror map [FJRW rings and Landau-Ginzburg mirror symmetry. Ann Arbor, MI: University of Michigan (PhD Thesis) (2010)].

MSC:

14J33 Mirror symmetry (algebro-geometric aspects)
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References:

[1] V.V. Batyrev - L.A. Borisov, On Calabi-Yau complete intersections in toric varieties, Higher-dimensional complex varieties (Trento, 1994), de Gruyter, Berlin, 1996, pp. 39–65. · Zbl 0908.14015
[2] P. Berglund - T. Hübsch, A generalized construction of mirror manifolds, Nuclear Phys. B 393 no. 1-2 (1993), 377–391. · Zbl 1245.14039
[3] L.A. Borisov, Berglund-Hübsch mirror symmetry via vertex algebras, Comm. Math. Phys. 320 no. 1 (2013), 73–99. · Zbl 1317.17032
[4] A. Chiodo - J. Nagel, The hybrid Landau-Ginzburg models of Calabi-Yau complete intersections, ArXiv e-prints (2015).
[5] A. Chiodo - Y. Ruan, LG/CY correspondence: the state space isomorphism, Adv. Math. 227 no. 6 (2011), 2157–2188. · Zbl 1245.14038
[6] E. Clader - Y. Ruan, Mirror Symmetry Constructions, ArXiv e-prints (2014).
[7] H. Fan - T. Jarvis - Y. Ruan, The Witten equation, mirror symmetry, and quantum singularity theory, Ann. of Math. (2) 178 no. 1 (2013), 1–106. · Zbl 1310.32032
[8] H. Fan - T. Jarvis - Y. Ruan, A Mathematical Theory of the Gauged Linear Sigma Model, ArXiv e-prints (2015).
[9] M. Krawitz, FJRW rings and Landau-Ginzburg mirror symmetry, ProQuest LLC, Ann Arbor, MI, 2010, Thesis (Ph.D.)–University of Michigan.
[10] A. Libgober, Elliptic genus of phases of N = 2 theories, Comm. Math. Phys. 340 no. 3 (2015), 939–958. · Zbl 1326.81181
[11] A. Libgober - J. Teitelbaum, Lines on Calabi-Yau complete intersections, mirror symmetry, and Picard-Fuchs equations, Internat. Math. Res. Notices no. 1 (1993), 29–39. · Zbl 0789.14005
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