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The $P=W$ identity for cluster varieties

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arxiv 1903.07014 v1 pith:F7ODPOOR submitted 2019-03-17 math.AG

Zili Zhang This is my paper · ORCID
classification math.AG
keywords varietiesclusterellipticexamplesfibrationsfiltrationidentityarise
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abstract

We find new examples of the $P=W$ identity 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.

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  1. Torus fibers and the weight filtration

    math.AG 2019-08 conditional novelty 7.0 of 10

    A single real torus inside a log Calabi-Yau complement (or a Calabi-Yau degeneration) computes the odd weight filtration, yielding P=W type results for rational surfaces and K3 surfaces.

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