Homological Berglund-Hübsch mirror symmetry for curve singularities

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-Hübsch 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.

34 pages, 17 figures. Comments welcome. v2 Minor updates. v3 Incorporates referee comments. To appear in Journal of Symplectic Geometry