SYZ mirror of Hirzebruch surface $\mathbb{F}_k$ and Morse homotopy
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914588935585792 |
|---|---|
| author | Nakanishi, Hayato |
| author_facet | Nakanishi, Hayato |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_01329 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | SYZ mirror of Hirzebruch surface $\mathbb{F}_k$ and Morse homotopy Nakanishi, Hayato Symplectic Geometry Algebraic Geometry Differential Geometry 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. |
| title | SYZ mirror of Hirzebruch surface $\mathbb{F}_k$ and Morse homotopy |
| topic | Symplectic Geometry Algebraic Geometry Differential Geometry |
| url | https://arxiv.org/abs/2312.01329 |