Locally complete intersection Stanley-Reisner ideals

TL;DR

This paper proves that for connected simplicial complexes of dimension at least 2, being locally complete intersection implies the Stanley-Reisner ideal is a complete intersection, with applications to Buchsbaum powers.

Contribution

It establishes a new characterization linking local properties of simplicial complexes to the global algebraic structure of their Stanley-Reisner ideals.

Findings

Stanley-Reisner ideal of certain complexes is a complete intersection

Powers of Stanley-Reisner ideals being Buchsbaum implies they are complete intersections

Connects local geometric conditions to algebraic ideal properties

Abstract

In this paper, we prove that the Stanley--Reisner ideal of any connected simplicial complex of dimension $\ge 2$ that is locally complete intersection is a complete intersection ideal. As an application, we show that the Stanley--Reisner ideal whose powers are Buchsbaum is a complete intersection ideal.