Pure parts of the mixed Hodge structures of character varieties of indivisible type

2014/06/11 by Arata Komyo, Komyo, Arata
Mathematics · #14C30 #14D20 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1406.2853

openalex publication_date 2014/06/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We fix integers k> 0 and n>0. For a k-punctured Riemann surface Σ∖ \ p₁,…,p_k \ and a k-tuple \boldsymbolμ=(μ¹,…,μ^k) of partitions of n, we can define the character variety of type \boldsymbolμ. In this paper, we consider the case where Σ=ℙ¹ and \boldsymbolμ is indivisible (i.e. g.c.d.(\boldsymbolμ)=1). For the case, we prove the purity conjecture due to Hausel, that is, the pure parts of the mixed Hodge structures of the character variety is isomorphic to the ordinary rational cohomology groups of the quiver variety of type \boldsymbolμ.

Related

• Topology of character varieties and representations of quivers
• On the types of the mixed Hodge structures of character varieties
• Cell decompositions of character varieties
• Mixed Hodge polynomials of character varieties
• Cohomology rings of character varieties