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arXiv · 2112.13537

Family Floer superpotential's critical values are eigenvalues of quantum product by $c_1$

Hang Yuan
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Abstract

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).

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Hang Yuan. 2021-12-27. Family Floer superpotential's critical values are eigenvalues of quantum product by $c_1$. https://doi.org/10.1007/s00029-024-01012-7

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