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Hodge polynomials of the SL(2, ℂ)-character variety of an elliptic curve with two marked points

Marina Logares

Instituto de Ciencias Matemáticas (CSIC-UAM-UC3M-UCM), C/Nicolas Cabrera 15, 28049 Madrid, Spain

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and

Vicente Muñoz

Instituto de Ciencias Matemáticas (CSIC-UAM-UC3M-UCM), C/Nicolas Cabrera 15, 28049 Madrid, Spain

Facultad de Matemáticas, Universidad Complutense de Madrid, Plaza Ciencias 3, 28040 Madrid, Spain

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https://doi.org/10.1142/S0129167X14501250Cited by:7 (Source: Crossref)

Abstract

We compute the Hodge polynomials for the moduli space of representations of an elliptic curve with two marked points into SL(2, ℂ). When we fix the conjugacy classes of the representations around the marked points to be diagonal and of modulus one, the character variety is diffeomorphic to the moduli space of strongly parabolic Higgs bundles, whose Betti numbers are known. In that case we can recover some of the Hodge numbers of the character variety. We extend this result to the moduli space of doubly periodic instantons.

Keywords:

AMSC: 14D20, 14C30, 14L24

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