Family Floer program and non-archimedean SYZ mirror construction

Fuente: arXiv
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Autore principale: Yuan, Hang
Natura: Preprint
Pubblicazione: 2020
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author Yuan, Hang
author_facet Yuan, Hang
contents 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 $A_\infty$ 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.
format Preprint
id arxiv_https___arxiv_org_abs_2003_06106
institution arXiv
publishDate 2020
record_format arxiv
spellingShingle Family Floer program and non-archimedean SYZ mirror construction
Yuan, Hang
Symplectic Geometry
Algebraic Geometry
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 $A_\infty$ 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.
title Family Floer program and non-archimedean SYZ mirror construction
topic Symplectic Geometry
Algebraic Geometry
url https://arxiv.org/abs/2003.06106