Hodge polynomials of SL (2,C)-character varieties for curves of small genus
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2013
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Springer
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Logares Jiménez, M., Muñoz Velázquez, V. & Newstead, P. E. «Hodge Polynomials of SL $$(2,\mathbb{C })$$ -Character Varieties for Curves of Small Genus». Revista Matemática Complutense, vol. 26, n.o 2, julio de 2013, pp. 635-703. DOI.org (Crossref), https://doi.org/10.1007/s13163-013-0115-5.
Abstract
We compute the E-polynomials of the moduli spaces of representations of the fundamental group of a complex curve into for the case of small genus and allowing the holonomy around a fixed point to be any matrix of that is 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 E-polynomial under fibrations