SYZ mirror of Hirzebruch surface ${\mathbb{F}}_k$ and Morse homotopy

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.

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

References in corpus (2)

• Homological mirror symmetry of $\mathbb{C}{P}^n$ and their products via Morse homotopy
• Homological mirror symmetry of toric Fano surfaces via Morse homotopy