On the symbolic $F$-splitness of binomial edge ideals

TL;DR

This paper investigates the symbolic $F$-splitness and strong $F$-regularity of binomial edge ideals and their symbolic blowup algebras using Fedder-like criteria and graph combinatorics.

Contribution

It introduces new criteria and methods for analyzing the $F$-splitness and $F$-regularity of binomial edge ideals based on graph properties.

Findings

Characterization of symbolic $F$-splitness for certain binomial edge ideals

Conditions for strong $F$-regularity of symbolic blowup algebras

Application of Fedder-like criteria to graph-based ideals

Abstract

We study the symbolic $F$-splitness of families of binomial edge ideals. We also study the strong $F$-regularity of the symbolic blowup algebras of families of binomial edge ideals. We make use of Fedder-like criteria and combinatorial properties of the graphs associated to the binomial edge ideals in order to approach the aforementioned scenarios.