Hodge-Deligne polynomials of SL(2,C)-character varieties for curves of small genus

2011/06/29 by Marina Logares, Logares, Marina, Vicente Mu ̃ Noz +3
Mathematics · #14D20 (Primary) 14C30 #14L24 #32J25 (Secondary) #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1106.6011

openalex publication_date 2011/06/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We compute the Hodge-Deligne polynomials of the moduli spaces of representations of the fundamental group of a complex surface into SL(2,C), for the case of small genus g, and allowing the holonomy around a fixed point to be any matrix of SL(2,C), that is Id, -Id, diagonalisable, or of either of the two Jordan types. For this, we introduce a new geometric technique, based on stratifying the space of representations, and on the analysis of the behaviour of the Hodge-Deligne polynomial under fibrations.

Citations

• The Self-Duality Equations on a Riemann Surface
• On the E-polynomials of a family of Character Varieties
• Topology of Hitchin systems and Hodge theory of character varieties: the case A₁

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• On Hodge polynomials of Singular Character Varieties
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