first of all, i will explain our variable-splitting theorems (j. korean math. soc. 37 (2000), no. 2, 245--251 and ann. sc. norm. super. pisa cl. sci. (5) 2 (2003), no. 3, 433--448). then i will formulate a generalization of our theorems as a parameter version. since i believe that segre variety mapping is a useful tool to attack the problem, i will give you an another proof of kim-zaitsev-a.h. theorem, which appears in above second mentioned paper.