E-polynomial of SL(2,C)-character varieties of complex curves of genus 3

2014/05/28 by Javier Martínez, Vicente Muñoz, Martinez, Javier +1 · 1 citation
Mathematics · #Algebraic Geometry and Number Theory #Advanced Algebra and Geometry #Finite Group Theory Research

paper · pdf · doi:10.48550/arxiv.1405.7120

Abstract

We compute the E-polynomials of the moduli spaces of representations of the fundamental group of a complex curve of genus g=3 into SL(2,C), and also of the moduli space of twisted representations. The case of genus g=1,2 has already been done in [http://arxiv.org/abs/1106.6011]. We follow the geometric technique introduced in [http://arxiv.org/abs/1106.6011], based on stratifying the space of representations, and on the analysis of the behaviour of the E-polynomial under fibrations.

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