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Toric degenerations of cluster varieties and cluster duality
We introduce the notion of a $Y$ -pattern with coefficients and its geometric counterpart: an $\mathcal {X}$ -cluster variety with coefficients. We use these constructions to build a flat degeneration of every skew-symmetrizable specially completed $\mathcal {X}$ -cluster variety $\widehat {\mathcal {X} }$ to the toric variety associated to its …