Family Floer superpotential's critical values are eigenvalues of quantum product by $c_1$
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arXiv
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866929646942027776 |
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| author | Yuan, Hang |
| author_facet | Yuan, Hang |
| contents | In the setting of the non-archimedean SYZ mirror construction (arXiv:2003.06106), we prove the folklore conjecture that the critical values of the mirror superpotential are the eigenvalues of the quantum multiplication by the first Chern class. Our result relies on a weak unobstructed assumption, but it is usually ensured in practice by Solomon's results on anti-symmetric Lagrangians. Lastly, we note that some explicit examples are presented in the recent work (arXiv:2206.04652). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2112_13537 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Family Floer superpotential's critical values are eigenvalues of quantum product by $c_1$ Yuan, Hang Symplectic Geometry Algebraic Geometry Quantum Algebra 53D37, 53D40, 53D45 In the setting of the non-archimedean SYZ mirror construction (arXiv:2003.06106), we prove the folklore conjecture that the critical values of the mirror superpotential are the eigenvalues of the quantum multiplication by the first Chern class. Our result relies on a weak unobstructed assumption, but it is usually ensured in practice by Solomon's results on anti-symmetric Lagrangians. Lastly, we note that some explicit examples are presented in the recent work (arXiv:2206.04652). |
| title | Family Floer superpotential's critical values are eigenvalues of quantum product by $c_1$ |
| topic | Symplectic Geometry Algebraic Geometry Quantum Algebra 53D37, 53D40, 53D45 |
| url | https://arxiv.org/abs/2112.13537 |