We study homological mirror symmetry for Hirzebruch surfaces Fk as complex manifolds by using the Strominger-Yau-Zaslow construction of mirror pair and Morse homotopy. For toric Fano surfaces, Futaki-Kajiura and the author proved homological mirror symmetry by using Morse homotopy in [9], [10], [16]. In this paper, we extend Futaki-Kajiura's result of the Hirzebruch surface F1 to Fk. We discuss Morse homotopy and show that homological mirror symmetry in the sense above holds true.
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H Nakanishi (2024) studied this question.
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