A combinatorial calculation of the Landau–Ginzburg model $$M={\mathbb {C}}^{3},W=z_1 z_2 z_3$$
Tóm tắt
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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