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- W4297564915 abstract "Let $Delta$ be a simplicial complex on $V = {x_1,...,x_n}$, with Stanley-Reisner ideal $I_{Delta}subseteq R = k[x_1,...,x_n]$. The goal of this paper is to investigate the class of artinian algebras $A=A(Delta,a_1,...,a_n)= R/(I_{Delta},x_1^{a_1},...,x_n^{a_n})$, where each $a_i geq 2$. By utilizing the technique of Macaulay's inverse systems, we can explicitly describe the socle of $A$ in terms of $Delta$. As a consequence, we determine the simplicial complexes, that we will call {em levelable}, for which there exists a tuple $(a_1,...,a_n)$ such that $A(Delta,a_1,...,a_n)$ is a level algebra." @default.
- W4297564915 created "2022-09-29" @default.
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- W4297564915 date "2007-12-11" @default.
- W4297564915 modified "2023-09-24" @default.
- W4297564915 title "Simplicial complexes and Macaulay's inverse systems" @default.
- W4297564915 doi "https://doi.org/10.48550/arxiv.0712.1804" @default.
- W4297564915 hasPublicationYear "2007" @default.
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