The P = W identity for cluster varieties

We find new examples of the P = W identities of de Cataldo-Hausel-Migliorini by studying cluster varieties. We prove that the weight filtration of 2D cluster varieties correspond to the perverse filtration of elliptic fibrations which are deformation equivalent to the elliptic fibrations of types I-b or 2I(b). These examples do not arise from character varieties or moduli of Higgs bundles.

Automated summary

By studying cluster varieties, new examples of the P = W identities of de Cataldo-Hausel-Migliorini are discovered. It is proven that the weight filtration of 2D cluster varieties corresponds to the perverse filtration of elliptic fibrations that are equivalent to certain types of elliptic fibrations. These examples do not originate from character varieties or moduli of Higgs bundles.