论文标题
Artinian Gorenstein嵌入维度四和Socle学位的代数
Artinian Gorenstein algebras of embedding dimension four and socle degree three
论文作者
论文摘要
We prove that in the polynomial ring $Q=\mathsf{k}[x,y,z,w]$, with $\mathsf{k}$ an algebraically closed field of characteristic zero, all Gorenstein homogeneous ideals $I$ such that $(x,y,z,w)^4\subseteq I \subseteq (x,y,z,w)^2$ can be由\ emph {倍加倍}从三年级的理想$ j \ subset i $获得，因此$ q/j $是本地的戈伦斯坦戒指。此外，可以完全描述$ q $ -module $ q/i $的分级最小自由分辨率，以$ q $ -module $ q/j $的分级最小免费分辨率以及规范模块$ω_{q/j} $ q/q/j $的均匀嵌入。
We prove that in the polynomial ring $Q=\mathsf{k}[x,y,z,w]$, with $\mathsf{k}$ an algebraically closed field of characteristic zero, all Gorenstein homogeneous ideals $I$ such that $(x,y,z,w)^4\subseteq I \subseteq (x,y,z,w)^2$ can be obtained by \emph{doubling} from a grade three perfect ideal $J\subset I$ such that $Q/J$ is a locally Gorenstein ring. Moreover, a graded minimal free resolution of the $Q$-module $Q/I$ can be completely described in terms of a graded minimal free resolution of the $Q$-module $Q/J$ and a homogeneous embedding of a shift of the canonical module $ω_{Q/J}$ into $Q/J$.
