Rees algebra and special fiber ring of binomial edge ideals of closed graphs

TL;DR

This paper investigates the algebraic properties and regularity bounds of Rees algebras and special fiber rings associated with binomial edge ideals of closed graphs, providing new bounds and insights.

Contribution

It introduces bounds for the regularity of Rees algebras and special fiber rings of binomial edge ideals of closed graphs, and explores their algebraic properties using Sagbi basis theory.

Findings

Lower bound for Rees algebra regularity

Upper bound for special fiber ring regularity

Analysis of algebraic properties via initial algebra and Sagbi basis

Abstract

In this article, we compute the regularity of Rees algebra of binomial edge ideals of closed graphs. We obtain a lower bound for the regularity of Rees algebra of binomial edge ideals. We also study some algebraic properties of the Rees algebra and special fiber ring of binomial edge ideals of closed graphs via algebraic properties of their initial algebra and Sagbi basis theory. We obtain an upper bound for the regularity of the special fiber ring of binomial edge ideals of closed graphs.