MIXED HODGE STRUCTURES OF THE MODULI SPACES OF PARABOLIC CONNECTIONS
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In this paper, we investigate the mixed Hodge structures of the moduli space of $\boldsymbol{\unicode[STIX]{x1D6FC}}$-stable parabolic Higgs bundles and the moduli space of $\boldsymbol{\unicode[STIX]{x1D6FC}}$-stable regular singular parabolic connections. We show that the mixed Hodge polynomials are independent of the choice of generic eigenvalues and the mixed Hodge structures of these moduli spaces are pure. Moreover, by the Riemann–Hilbert correspondence, the Poincaré polynomials of character varieties are independent of the choice of generic eigenvalues.
2007 ◽
Vol 18
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pp. 695-721
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1991 ◽
Vol 06
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pp. 1749-1813
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2010 ◽
Vol 198
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pp. 173-190
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2020 ◽
Vol 221
(1)
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pp. 301-327
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2014 ◽
Vol 25
(14)
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pp. 1450125
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