Arata Komyo
Nagoya Mathematical Journal, 225 185-206, Mar, 2017 Peer-reviewed
In this paper, we investigate the mixed Hodge structures of the moduli space of alpha-stable parabolic Higgs bundles and the moduli space of a-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 Poincare polynomials of character varieties are independent of the choice of generic eigenvalues.