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arXiv · 1903.01351

Homological Berglund-H\"ubsch mirror symmetry for curve singularities

Matthew Habermann·Jack Smith
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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.

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Matthew Habermann, Jack Smith. 2019-03-04. Homological Berglund-H\"ubsch mirror symmetry for curve singularities. https://arxiv.org/abs/1903.01351

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