Infinitesimal deformations of parabolic connections and parabolic opers

Abstract

We compute the infinitesimal deformations of quadruples $(X,S,E_{\ast },D)$, where $(X,S)$ is a compact Riemann surface with $n$ marked points, $E_{\ast }$ is a parabolic vector bundle on $X$ with parabolic structure over $S$, and $D$ is a parabolic connection on $E_{\ast }$. Using it we compute the infinitesimal deformations of $(X,S,D)$, where $D$ is a parabolic SL(r, C)-oper on $(X,S)$. It is shown that the monodromy map, from the moduli space of triples $(X,S,D)$, where $D$ is a parabolic SL(r, C)-oper on $(X,S)$, to the SL(r, C)-character variety of X - S, is an immersion.

final version