Homological Berglund-H\"ubsch mirror symmetry for curve singularities
Symplectic Geometry
2020-03-13 v3 Algebraic Geometry
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 -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.
Keywords
Cite
@article{arxiv.1903.01351,
title = {Homological Berglund-H\"ubsch mirror symmetry for curve singularities},
author = {Matthew Habermann and Jack Smith},
journal= {arXiv preprint arXiv:1903.01351},
year = {2020}
}
Comments
34 pages, 17 figures. Comments welcome. v2 Minor updates. v3 Incorporates referee comments. To appear in Journal of Symplectic Geometry