Retracts and algebraic properties of cut algebras

TL;DR

This paper investigates the algebraic properties of cut algebras derived from graphs, using retracts to analyze invariants like complete intersection status, linear resolutions, and regularity.

Contribution

It introduces a novel approach using retracts to study algebraic invariants of cut algebras associated with graphs.

Findings

Identification of conditions for cut algebras to be complete intersections

Criteria for having linear resolutions in cut algebras

Insights into Castelnuovo-Mumford regularity of these algebras

Abstract

We study cut algebras which are toric rings associated to graphs. The key idea is to consider suitable retracts to understand algebraic properties and invariants of such algebras like being a complete intersection, having a linear resolution, or the Castelnuovo-Mumford regularity. Throughout the paper, we discuss several examples and pose some problems as well.