Explicit description of jumping phenomena on moduli spaces of parabolic   connections and Hilbert schemes of points on surfaces
  In this paper, we investigate the apparent singularities and the dual parameters of rank 2 parabolic connections on $\mathbb{P}^1$ and rank 2 (parabolic) Higgs bundle on $\mathbb{P}^1$. Then we obtain explicit descriptions of Zariski open sets of the moduli space of the parabolic connections and the moduli space of the Higgs bundles. For $n=5$, we can give global descriptions of the moduli spaces in detail. 
Arata Komyo and Masa-Hiko Saito
math.AG