Simplicial complexes and Macaulay’s inverse systems

Authors

Adam Van Tuyl, Lakehead University
Fabrizio Zanello, Michigan Technological UniversityFollow

Document Type

Article

Publication Date

5-2010

Abstract

Let Δ be a simplicial complex on V = {x ₁, . . . , x _n }, with Stanley–Reisner ideal IΔ⊆R=k[x₁,…,x_n] . The goal of this paper is to investigate the class of artinian algebras A=A(Δ,a₁,…,a_n)=R/(IΔ,x^a₁¹,…,x^a_nⁿ) , where each a _i ≥ 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 the simplicial complexes, that we will call levelable, for which there exists a tuple (a ₁, . . . , a _n ) such that A(Δ, a ₁, . . . , a _n ) is a level algebra.

Publisher's Statement

© Springer-Verlag 2009. Publisher’s version of record: https://doi.org/10.1007/s00209-009-0507-x

Publication Title

Mathematische Zeitschrift

Recommended Citation

Van Tuyl, A., & Zanello, F. (2010). Simplicial complexes and Macaulay’s inverse systems. Mathematische Zeitschrift, 265(1), 151-160. http://doi.org/10.1007/s00209-009-0507-x
Retrieved from: https://digitalcommons.mtu.edu/math-fp/46