Abstract: Joint with Louis Funar. Motivated by the study of certain algebraic surfaces that were proposed as candidates to be  counter examples to the Shafarevich conjecture on holomorphic convexity by Bogomolov and Katzrakov in 1998,  we introduce an orbifold compactification of the moduli stack of pointed curves so that TQFT representations of the mapping class groups define representations of the fundamental group. This enables to settle these examples and to show in general that they satisfy the conjecture.