Some results on the variety of complexes

Let R be a (commutative) Noetherian ring, and let {n 0 , n 1 …, n m } {k 1 k 2 , …, k m } be two sequences of integers satisfying m > 0, k i ≧ 0 ( i = 1, 2, …, m ) and n i ≧ k i k i + 1 ( i = 1, 2, …, m ) with k 0 = k m + 1 = 0.