Simplicial complexes and Macaulay’s inverse systems

Let Δ be a simplicial complex on V = {x1, . . . , xn}, with Stanley–Reisner ideal $${I_{\Delta}\subseteq R=k[x_1,\ldots, x_n]}$$ . The goal of this paper is to investigate the class of artinian algebras $${A=A(\Delta,a_1,\ldots,a_n)= R/(I_{\Delta},x_1^{a_1},\ldots,x_n^{a_n})}$$ , where each ai ≥ 2. By utilizing the technique of Macaulay’s inverse systems, we can explicitly describe the socle of A in terms of Δ. As a consequence, we determine …