Hodge polynomials of SL $$(2,\mathbb{C })$$ -character varieties for curves of small genus

Arapura, D.: The Leray spectral sequence is motivic. Invent. Math. 160, 567–589 (2005)

Boden, H., Yokogawa, K.: Moduli spaces of parabolic Higgs bundles and parabolic K(D) pairs over smooth curves: I. Int. J. Math. 7, 573–598 (1996)

de Cataldo, A., Hausel, T., Migliorini, L.: Topology of Hitchin systems and Hodge theory of character varieties: the case $$A_{1}$$ . Ann. Math. (2) 175(3), 1329–1407 (2012)

Corlette, K.: Flat $$G$$ -bundles with cannonical metrics. J. Diff. Geom. 28, 361–382 (1988)

Deligne, P.: Équations différentielles á points singuliers réguliers. In: Lecture Notes in Mathematics, vol. 163. Springer, Berlin (1970)

Deligne, P.: Théorie de Hodge II. Publ. Math. I.H.E.S. 40, 5–5 (1971)

Deligne, P.: Théorie de Hodge III. Publ. Math. I.H.E.S. 44, 5–77 (1974)

Donaldson, S.: Twisted harmonic maps and the self duality equations. Proc. Lond. Math. Soc. 55, 127–131 (1987)

García-Prada, O., Gothen, P.B., Muñoz, V.: Betti numbers of the moduli space of rank 3 parabolic Higgs bundles. Mem. Am. Math. Soc. 187, viii+80 (2007)

García-Prada, O., Heinloth, J., Schmitt, A.: On the motives of moduli of chains and Higgs bundles, preprint, arXiv:1104.5558

Gothen, P.B.: The Betti numbers of the moduli space of rank 3 Higgs bundles. Int. J. Math. 5, 861–875 (1994)

Hausel, T.: Mirror symmetry and Langlands duality in the non-Abelian Hodge theory of a curve, Geometric methods in algebra and number theory, pp. 193–217. In: Progr. Math., vol. 235. Birkhauser, Basel (2005)

Hausel, T., Letellier, E., Rodriguez-Villegas, F.: Arithmetic harmonic analysis on character and quiver varieties. Duke Math. J. 160(2), 323–400 (2011)

Hausel, T.: Rodriguez Villegas, F.: Mixed Hodge polynomials of character varieties. Invent. Math. 174, 555–624 (2008)

Hausel, T., Thaddeus, M.: Mirror symmetry, Langlands duality and Hitchin systems. Invent. Math. 153, 197–229 (2003)

Hitchin, N.J.: The self-duality equations on a Riemann surface. Proc. Lond. Math. Soc. 55(3), 59–126 (1987)

Hitchin, N.J.: Stable bundles and integrable systems. Duke Math. J. 54, 91–114 (1987)

Mereb, M.: On the E-polynomials of a family of Character Varieties, Ph. D. dissertation, arXiv:1006.1286

Mehta, M.: Hodge structure on the cohomology of the moduli space of Higgs bundles, preprint, arXiv:math.AG/0112111

Muñoz, V., Ortega, D., Vázquez-Gallo, M.-J.: Hodge polynomials of the moduli space of pairs. Int. J. Math. 18, 695–721 (2007)

Muñoz, V., Ortega, D., Vázquez-Gallo, M.-J.: Hodge polynomials of the moduli space of triples of rank (2,2). Q. J. Math. 60, 235–272 (2009)

Muñoz, V.: The $$SL(2,{\mathbb{C}})$$ -character varieties of torus knots. Rev. Mat. Complut. 22, 489–497 (2009)

Peters, C., Steenbrink, J.: Mixed Hodge Structures, vol. 52. Springer, Berlin (2007)

Simpson, C.: Constructing variations of Hodge structure using Yang-Mills theory and applications to uniformization. J. Am. Math. Soc. 1, 867–918 (1988)

Simpson, C.: Higgs bundles and local systems. Inst. Hautes Études Sci. Publ. Math. 75, 5–95 (1992)

Simpson, C.: Moduli space of representations of the fundamental group of a smooth projective variety II. Inst. Hautes Études Sci. Publ. Math. 80, 5–79 (1995)

Simpson, C.: Harmonic bundles on noncompact curves. J. Am. Math. Soc. 3, 713–770 (1990)