학술논문
SYZ mirror of Hirzebruch surface $\mathbb{F}_k$ and Morse homotopy
Document Type
Working Paper
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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.
Comment: 19 pages, 4 figures. arXiv admin note: substantial text overlap with arXiv:2303.07851; text overlap with arXiv:2012.06801 by other authors
Comment: 19 pages, 4 figures. arXiv admin note: substantial text overlap with arXiv:2303.07851; text overlap with arXiv:2012.06801 by other authors