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

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

2011-06-29

arxiv.org/abs/1106.6011v3

Mathematics

Algebraic Geometry

60 pages, 3 figures. Proposition 2.10 has been corrected. Other minor changes added

Scientific paper

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.

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