Cohomology of cluster varieties. II. Acyclic case

2021/11/24 by Thomas Lam, David E Speyer, Lam, Thomas +1 · 2 citations
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2111.12759

openalex publication_date 2021/11/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In previous work, we initiated the study of the cohomology of locally acyclic cluster varieties. In the present work, we show that the mixed Hodge structure and point counts of acyclic cluster varieties are essentially determined by the combinatorics of the independent sets of the quiver. We use this to show that the mixed Hodge numbers of acyclic cluster varieties of really full rank satisfy a strong vanishing condition.

Cited by

• Cluster tori over \mathbbF₂, hexagonal moves on triangulations, and minimal coverings of cluster manifolds
• Mixed Hodge Structures of cluster varieties of dimension 3

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