Mirror Symmetry for Truncated Cluster Varieties

Abstract: Gross, Hacking and Keel gave an algebro-geometric construction of cluster varieties: take a toric variety, blow up appropriate subvarieties in the boundary, and then remove the strict transform of the boundary. We work with a modification of this construction, which we call a truncated cluster variety--roughly, this comes from performing the same procedure on the toric variety with all the codimension 2 strata removed. The resulting variety differs from the cluster variety in codimension 2. I will describe a construction of a Weinstein manifold mirror to a truncated cluster variety and explain how to prove a mirror symmetry via Lagrangian skeleta. We hope that this is a first step towards understanding mirror symmetry for the entire cluster variety. This is joint work with Benjamin Gammage.

algebraic geometrydifferential geometrygeometric topologysymplectic geometry

Audience: researchers in the topic

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