Here we prove the following result. Fix integersq, τ,a’, b’, a’ i, 1≤i≤τ,a’, b’,
a’ i, 1≤i≤τ; then there is an integerew such that for every integert≥w, for
every algebraically closed fieldK for every smooth complete surfaceX with
negative Kodaira dimension, irregularityq andK 2 =8(1−q)−τ, the following
condition holds; ifX→S is a sequence fo τ blowing-downs which gives a relatively
minimal model ... hiện toàn bộ