Buchsbaum homogeneous algebras with minimal multiplicity

Abstract: In this paper we first give a lower bound on multiplicities for Buchsbaum homogeneous -algebras in terms of the dimension , the codimension , the initial degree , and the length of the local cohomology modules of . Next, we introduce the notion of Buchsbaum -algebras with minimal multiplicity of degree , and give several characterizations for those rings. In particular, we will show that those algebras have linear free resolutions. Further, we will give many examples of those algebras. [Copyright &y& Elsevier]