Mirror symmetry for the Landau-Ginzburg A-model $M={\mathbb{C}}^n,W=z_1\cdots z_n$

Abstract

We calculate the category of branes in the Landau-Ginzburg A-model with background $M={\mathbb{C}}^n$ and superpotential $W=z_1\cdots z_n$ in the form of microlocal sheaves along a natural Lagrangian skeleton. Our arguments employ the framework of perverse schobers, and our results confirm expectations from mirror symmetry.

53 pages; minor expository changes, updated references

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• Homological mirror symmetry for hypertoric varieties II (with an Appendix written jointly with Laurent Côté and Justin Hilburn)