Abstract:We study homological mirror symmetry for Hirzebruch surface $\mathbb{F}_k$ as a complex manifold by using the Strominger-Yau-Zaslow construction of mirror pair and Morse homotopy. For the toric Fano surfaces, Futaki-Kajiura and the author proved homological mirror symmetry by using Morse homotopy in arXiv:2008.13462, arXiv:2012.06801, and arXiv:2303.07851. In this paper, we extend Futaki-Kajiura's result of Hirzebruch surface $\mathbb{F}_1$ to $\mathbb{F}_k$. We discuss Morse homotopy and show homological mirror symmetry in the sense above holds true.
| Comments: | v2: 19 pages, 4 figures. Fixed typos. arXiv admin note: substantial text overlap with arXiv:2303.07851; text overlap with arXiv:2012.06801 by other authors |
| Subjects: | Symplectic Geometry (math.SG); Algebraic Geometry (math.AG); Differential Geometry (math.DG) |
| Cite as: | arXiv:2312.01329 [math.SG] |
| (or arXiv:2312.01329v2 [math.SG] for this version) | |
| https://doi.org/10.48550/arXiv.2312.01329 arXiv-issued DOI via DataCite |
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| Journal reference: | Journal of Geometry and Physics, Volume 204 (2024) |
| Related DOI: | https://doi.org/10.1016/j.geomphys.2024.105255
DOI(s) linking to related resources |
From: Hayato Nakanishi [view email]
[v1]
Sun, 3 Dec 2023 09:36:29 UTC (15 KB)
[v2]
Fri, 22 May 2026 09:43:16 UTC (15 KB)
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