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arXiv · 2012.06801

Homological mirror symmetry of $\mathbb{F}_1$ via Morse homotopy

Masahiro Futaki·Hiroshige Kajiura
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Abstract

This is a sequel to our paper arXiv:2008.13462, where we proposed a definition of the Morse homotopy of the moment polytope of toric manifolds. Using this as the substitute of the Fukaya category of the toric manifolds, we proved a version of homological mirror symmetry for the projective spaces and their products via Strominger-Yau-Zaslow construction of the mirror dual Landau-Ginzburg model. In this paper we go this way further and extend our previous result to the case of the Hirzebruch surface $\mathbb{F}_1$.

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BibTeXRIS

Masahiro Futaki, Hiroshige Kajiura. 2020-12-12. Homological mirror symmetry of $\mathbb{F}_1$ via Morse homotopy. https://arxiv.org/abs/2012.06801

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