Habermann, M;
Smith, J;
(2020)
Homological Berglund-Hübsch mirror symmetry for curve singularities.
Journal of Symplectic Geometry
, 18
(6)
pp. 1515-1574.
10.4310/JSG.2020.v18.n6.a2.
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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–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.
| Type: | Article |
|---|---|
| Title: | Homological Berglund-Hübsch mirror symmetry for curve singularities |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.4310/JSG.2020.v18.n6.a2 |
| Publisher version: | https://dx.doi.org/10.4310/JSG.2020.v18.n6.a2 |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| Keywords: | Symplectic geometry |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/10101709 |
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