Family Floer program and non-archimedean SYZ mirror construction
Abstract
Given a Lagrangian fibration, we provide a natural construction of a mirror Landau-Ginzburg model consisting of a rigid analytic space, a superpotential function, and a dual fibration based on Fukaya's family Floer theory. The mirror in the B-side is constructed by the counts of holomorphic disks in the A-side together with the non-archimedean analysis and the homological algebra of the structures. It fits well with the SYZ dual fibration picture and explains the quantum/instanton corrections and the wall crossing phenomenon. Instead of a special Lagrangian fibration, we only need to assume a weaker semipositive Lagrangian fibration to carry out the non-archimedean SYZ mirror reconstruction.
Keywords
Cite
@article{arxiv.2003.06106,
title = {Family Floer program and non-archimedean SYZ mirror construction},
author = {Hang Yuan},
journal= {arXiv preprint arXiv:2003.06106},
year = {2025}
}
Comments
81 pages. Following the referee's suggestion, many secondary details, which should be recoverable by the reader, have been omitted to streamline the paper, while most essential details have been retained