Geodesic
Mirror Symmetry for Truncated Cluster Varieties
Symmetry, integrability and geometry: methods and applications, Tome 18 (2022) Cet article a éte moissonné depuis la source Math-Net.Ru

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In the algebraic setting, cluster varieties were reformulated by Gross–Hacking–Keel as log Calabi–Yau varieties admitting a toric model. Building on work of Shende–Treumann–Williams–Zaslow in dimension 2, we describe the mirror to the GHK construction in arbitrary dimension: given a truncated cluster variety, we construct a symplectic manifold and prove homological mirror symmetry for the resulting pair. We also describe how our construction can be obtained from toric geometry, and we relate our construction to various aspects of cluster theory which are known to symplectic geometers.
Keywords: homological mirror symmetry, cluster varieties, almost toric fibrations. 
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     author = {Benjamin Gammage and Ian Le},
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     url = {http://geodesic.mathdoc.fr/item/SIGMA_2022_18_a54/}
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Benjamin Gammage; Ian Le. Mirror Symmetry for Truncated Cluster Varieties. Symmetry, integrability and geometry: methods and applications, Tome 18 (2022). http://geodesic.mathdoc.fr/item/SIGMA_2022_18_a54/

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