Buchsbaum homogeneous algebras with minimal multiplicity
Abstract
In this paper we first give a lower bound on multiplicities for Buchsbaum homogeneous
k
-algebras
A
in terms of the dimension
d
, the codimension
c
, the initial degree
q
, and the length of the local cohomology modules of
A
. Next, we introduce the notion of Buchsbaum
k
-algebras with minimal multiplicity of degree
q
, 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.