The quadratic (Pfaffian) relations define a complete intersection variety Q in a ℙn of a-variables. In this procedure, we compute the loci of points in Q at which the rank of e-matrix drops, that is, the minimal primes of the maximal minors of the e-matrix (within the variety Q). These loci play an important role for the construction of surfaces with torsion groups ℤ/nℤ for n ≥3.