Abstract:Strominger-Yau-Zaslow (SYZ) proposed a way of constructing mirror pairs as pairs of torus fibrations. We apply this SYZ construction to toric Fano surfaces as complex manifolds, and discuss the homological mirror symmetry, where we consider Morse homotopy of the moment polytope instead of the Fukaya category.
| Comments: | v3: 50 pages, 5 figures, Fixed typos. arXiv admin note: text overlap with arXiv:2012.06801 by other authors |
| Subjects: | Differential Geometry (math.DG); Algebraic Geometry (math.AG); Symplectic Geometry (math.SG) |
| Cite as: | arXiv:2303.07851 [math.DG] |
| (or arXiv:2303.07851v3 [math.DG] for this version) | |
| https://doi.org/10.48550/arXiv.2303.07851 arXiv-issued DOI via DataCite |
|
| Journal reference: | J. Math. Phys. 65, 053501 (2024) |
| Related DOI: | https://doi.org/10.1063/5.0168792
DOI(s) linking to related resources |
From: Hayato Nakanishi [view email]
[v1]
Tue, 14 Mar 2023 12:46:42 UTC (27 KB)
[v2]
Thu, 6 Apr 2023 13:27:22 UTC (27 KB)
[v3]
Fri, 22 May 2026 09:42:49 UTC (28 KB)
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