Abstract
The aim of this paper is to apply ideas from the study of Legendrian singularities to a specific example of interest within mirror symmetry. We calculate the Landau–Ginzburg A-model with \(M={\mathbb {C}}^{3},W=z_1 z_2 z_3\) in its guise as microlocal sheaves along the natural singular Lagrangian thimble \(L={\hbox {Cone}}(T^2)\subset M\). The description we obtain is immediately equivalent to the B-model of the pair-of-pants \(\mathbb {P}^{1}{\setminus }\{0,1,\infty \}\) as predicted by mirror symmetry.
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Acknowledgments
I thank D. Auroux and E. Zaslow for suggesting the application studied in this paper. I also thank them as well as D. Ben-Zvi, M. Kontsevich, J. Lurie, N. Rozenblyum, V. Shende, N. Sheridan, D. Treumann, and H. Williams for their interest, encouragement, and valuable comments. Finally, I am grateful to the NSF for the support of grant DMS-1502178.
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Nadler, D. A combinatorial calculation of the Landau–Ginzburg model \(M={\mathbb {C}}^{3},W=z_1 z_2 z_3\) . Sel. Math. New Ser. 23, 519–532 (2017). https://doi.org/10.1007/s00029-016-0254-x
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DOI: https://doi.org/10.1007/s00029-016-0254-x