Family Floer program and non-archimedean SYZ mirror construction
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2020
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866909453243121664 |
|---|---|
| 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 |