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.

中文翻译：

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集群品种的 $P=W$ 标识

我们通过研究簇变体发现了 de Cataldo-Hausel-Migliorini 的 $P = W$ 恒等式的新例子。我们证明了二维簇品种的权重过滤对应于椭圆纤维的逆向过滤，椭圆纤维变形相当于 $I_b$ 或 $2I_b$ 类型的椭圆纤维变形。这些例子不是由希格斯丛的特征变体或模产生的。