Berglund–Hübsch homological mirror symmetry for invertible polynomials

Let WW be an invertible polynomial, let GG be a subgroup of its maximal symmetry group GWG_W, and let WTW^T and GTG^T be the transpose polynomial and transpose subgroup, respectively. Write F(W,G)\mathcal{F}(W,G) for the Fukaya category associated with (W,G)(W,G) and MF(WT,GT)\mathcal{MF}(W^T,G^T) for the GTG^T-equivariant matrix factorization category.

Berglund–Hübsch homological mirror symmetry conjecture. There exists a derived equivalence between F(W,G)\mathcal{F}(W,G) and MF(WT,GT)\mathcal{MF}(W^T,G^T).

This is the homological mirror symmetry prediction for Berglund–Hübsch dual pairs. The source indicates that homological mirror symmetry has been proved in related works by computation of both sides, so this formulation is recorded as solved.

Sources & referencesView supporting material

Primary source

Cheol-Hyun Cho, Dongwook Choa and Wonbo Jeong, “Berglund-Hübsch mirrors of invertible curve singularities via Floer theory”, arXiv:2410.14678 (2024).

Additional references

2 papers in this index state this conjecture (2020–2024). The statement above is taken from the most recent of them; the others are arXiv:2010.15570.

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