Homological mirror symmetry for the non-Calabi–Yau suspension

Let \bfW\bfW be an invertible polynomial not of Calabi--Yau type, let UU be the associated quotient stack, let \Uv\Uv be the corresponding Milnor fiber, and let \scohU\scoh U and \scoh0U\scoh_0 U denote the indicated singularity categories, with the latter consisting of objects supported at the origin. Non-Calabi–Yau suspension conjecture. For any such \bfW\bfW, there are equivalences

\scohU\wfuk\Uv\scoh U \simeq \wfuk{\Uv}

and

\scoh0U\fuk\Uv\scoh_0 U \simeq \fuk{\Uv}

of \infty-categories. This is a proposed categorical mirror-symmetry statement for the suspension construction; no resolution status is supplied in the source.

Sources & referencesView supporting material

Primary source

Yanki Lekili and Kazushi Ueda, “Rabinowitz Fukaya categories as cluster categories”, arXiv:2406.15915 (2026).

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