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Buchsbaum homogeneous algebras with minimal multiplicity

Shiro Goto·Ken-ichi Yoshida
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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.

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Shiro Goto, Ken-ichi Yoshida. 2006-07-18. Buchsbaum homogeneous algebras with minimal multiplicity. https://arxiv.org/abs/math/0607415

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