The singularities of Selberg- and Dotsenko-Fateev-like integrals

We discuss the meromorphic continuation of certain hypergeometric integrals modeled on the Selberg integral, including the 3-point and 4-point functions of BPZ’s minimal models of 2D CFT as described by Felder and Silvotti and Dotsenko and Fateev (the Coulomb gas formalism''). This is accomplished via a geometric analysis of the singularities of the integrands. In the case that the integrand is symmetric (as in the Selberg integral itself) or, more generally, what we call DF-symmetric,‘’ we show that a number of apparent singularities are removable, as required for the construction of the minimal models via these methods.