Abstract
is an invariant of A not depending on the choice of a parameter ideal q of A, where f,(A/q) and e,(q) denote, respectively, the length of the A-module A/q and the multiplicity of A relative to q (see Section 2 for detail). Here recall that if A is Buchsbaum, the local ring A, is Cohen-Macaulay and dim A, = d-dim A/p for any prime ideal p (p # m) of A. Moreover the local cohomology modules #,,(A) (i # d) of A are vector spaces, that is, m . H;(A) = (0) and one has the equality
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