Homological Berglund-Hübsch-Henningson mirror symmetry for curve singularities
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866908284307374080 |
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| author | Habermann, Matthew |
| author_facet | Habermann, Matthew |
| contents | In this article, we establish homological Berglund--Hübsch mirror symmetry for curve singularities where the A--model incorporates equivariance, otherwise known as homological Berglund--Hübsch--Henningson mirror symmetry, including for certain deformations of categories. More precisely, we prove a conjecture of Futaki and Ueda in arXiv:1004.0078 which posits that the equivariance in the A-model can be incorporated by pulling back the superpotential to the total space of the corresponding crepant resolution. Along the way, we show that the B--model category of matrix factorisations has a tilting object whose length is the dimension of the state space of the FJRW A--model, a result which might be of independent interest for its implications in the Landau--Ginzburg analogue of Dubrovin's conjecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2205_12947 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Homological Berglund-Hübsch-Henningson mirror symmetry for curve singularities Habermann, Matthew Symplectic Geometry Algebraic Geometry 53D37, 16G50 In this article, we establish homological Berglund--Hübsch mirror symmetry for curve singularities where the A--model incorporates equivariance, otherwise known as homological Berglund--Hübsch--Henningson mirror symmetry, including for certain deformations of categories. More precisely, we prove a conjecture of Futaki and Ueda in arXiv:1004.0078 which posits that the equivariance in the A-model can be incorporated by pulling back the superpotential to the total space of the corresponding crepant resolution. Along the way, we show that the B--model category of matrix factorisations has a tilting object whose length is the dimension of the state space of the FJRW A--model, a result which might be of independent interest for its implications in the Landau--Ginzburg analogue of Dubrovin's conjecture. |
| title | Homological Berglund-Hübsch-Henningson mirror symmetry for curve singularities |
| topic | Symplectic Geometry Algebraic Geometry 53D37, 16G50 |
| url | https://arxiv.org/abs/2205.12947 |