Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 306 / 3 / 1 / Solution

The three unintegrated vertices fix the residual Möbius symmetry of the sphere and saturate its three holomorphic and antiholomorphic ghost zero modes. Moving a fixed insertion changes the amplitude by a BRST-exact operator, whose expectation with physical BRST-closed vertices vanishes. The remaining integrated positions are dummy variables. Thus the amplitude is independent of the chosen coordinates $(z_i,{\bar{z}}_i)$.