Mixed Hodge Structures of cluster varieties of dimension 3

Yuhang Zhang; Zili Zhang

Mixed Hodge Structures of cluster varieties of dimension 3

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arxiv 2508.13752 v1 pith:IP65ILXD submitted 2025-08-19 math.AG

Yuhang Zhang , Zili Zhang This is my paper · ORCID

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keywords mixedclusterhodgevarietiescohomologystructurescalculatedimension

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We calculate the mixed Hodge numbers of smooth 3-dimensional cluster varieties and show that they are of mixed Tate type. We also study the mixed Hodge structures of the cohomology and intersection cohomology groups of some singular cluster varieties.

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A non-holomorphic P=W phenomenon
math.AG 2026-07 accept novelty 6.0 of 10

P=W and PI=WI hold for all 3D isolated cluster varieties, including singular non-full-rank ones, via explicit real-analytic perverse truncations and mixed Hodge modules.

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