This is explained in no 17 of Igusa's paper "On the theory of algebraic correspondences...", J. Math. Soc. Japan 1 (1949), DOI: 10.2969/jmsj/00120147; it corresponds to Felipe Voloch's guess.
(There are many typos in Igusa's paper, and the Project Euclid scan does not improve them. Better read a hard copy if possible.)
