English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We study homological mirror symmetry for Hirzebruch surface $\mathbb{F}_k$ asa complex manifold by using the Strominger-Yau-Zaslow construction of mirrorpair and Morse homotopy. For the toric Fano surfaces, Futaki-Kajiura and theauthor proved homological mirror symmetry by using Morse homotopy inarXiv:2008.13462, arXiv:2012.06801, and arXiv:2303.07851. In this paper, weextend Futaki-Kajiura's result of Hirzebruch surface $\mathbb{F}_1$ to$\mathbb{F}_k$. We discuss Morse homotopy and show homological mirror symmetryin the sense above holds true.

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