dd-Sequences and Partial Euler-Poincare' Characteristics of Koszul Complex

Nguyen Tu Cuong and Doan Trung Cuong


    The aim of this short note is to give new concept of sequences called dd-sequences, which is a slight generalization of the notion of unconditioned strong d-sequence. Then we apply these dd-sequences to stady the polynomial property of the lengths of Koszul homology and of local cohomology modules with respect to the powers of a system of parameters. A completion of all proofs of statements given here the readers can find in [3].