Buchsbaum homogeneous algebras with minimal multiplicity

In this paper we first give a lower bound on multiplicities for Buchsbaum homogeneous kk-algebras AA in terms of the dimension dd, the codimension cc, the initial degree qq, and the length of the local cohomology modules of AA. Next, we introduce the notion of Buchsbaum kk-algebras with minimal multiplicity of degree qq, 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.