Intersection cohomology of character varieties for punctured Riemann surfaces

2022/01/21 by Mathieu Ballandras, Ballandras, Mathieu · 1 citation
Mathematics · #14F43 #14M35 #Advanced Algebra and Geometry #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2201.08795

openalex publication_date 2022/01/21 · openalex created_date 2022/04/03 · openalex updated_date 2026/07/28

Abstract

We study intersection cohomology of character varieties for punctured Riemann surfaces with prescribed monodromies around the punctures. Relying on previous result from Mellit for semisimple monodromies we compute the intersection cohomology of character varieties with monodromies of any Jordan type. This proves the Poincaré polynomial specialization of a conjecture from Letellier.

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• The tame Deligne-Simpson problem

Related

• Intersection cohomology of rank two character varieties of surface groups
• Cell decompositions of character varieties
• Cohomology rings of character varieties
• Character varieties with Zariski closures of GL_n-conjugacy classes at punctures
• Intersection cohomology of higher rank Teichmüller components