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Homological Berglund-Hübsch mirror symmetry for curve singularities (1903.01351v3)
Published 4 Mar 2019 in math.SG and math.AG
Abstract: Given a two-variable invertible polynomial, we show that its category of maximally-graded matrix factorisations is quasi-equivalent to the Fukaya-Seidel category of its Berglund-H\"ubsch transpose. This was previously shown for Brieskorn-Pham and $D$-type singularities by Futaki-Ueda. The proof involves explicit construction of a tilting object on the B-side, and comparison with a specific basis of Lefschetz thimbles on the A-side.