Gorenstein liaison for toric ideals of graphs

TL;DR

This paper proves that toric ideals of edge subrings of bipartite graphs are in the G-liaison class of complete intersections, advancing understanding in liaison theory.

Contribution

It establishes that all such toric ideals are G-liaison equivalent to complete intersections, confirming a key conjecture for this class.

Findings

Toric ideals of bipartite graph edge subrings are G-liaison equivalent to complete intersections.

Supports the conjecture that Cohen-Macaulay ideals belong to the same G-liaison class as complete intersections.

Advances the understanding of liaison classes in algebraic geometry and combinatorics.

Abstract

A central question in liaison theory asks whether every Cohen-Macaulay, graded ideal of a standard graded K-algebra belongs to the same G-liaison class of a complete intersection. In this paper we answer this question positively for toric ideals defining edge subrings of bipartite graphs.