The Stanley-Reisner ideals of polygons as set-theoretic complete intersections

TL;DR

This paper proves that the Stanley-Reisner ideal of an n-gon simplicial complex is always a set-theoretic complete intersection across all positive characteristics, advancing understanding in combinatorial commutative algebra.

Contribution

It establishes that the Stanley-Reisner ideal of polygons is a set-theoretic complete intersection in any positive characteristic, a result previously unknown.

Findings

Stanley-Reisner ideal of polygons is a set-theoretic complete intersection

Result holds in all positive characteristics

Advances understanding of algebraic properties of simplicial complexes

Abstract

We show that the Stanley-Reisner ideal of the one-dimensional simplicial complex whose diagram is an $n$-gon is always a set-theoretic complete intersection in any positive characteristic.