Minimal Attached Primes of Local Cohomology Modules of Binomial Edge Ideals of Block Graphs

TL;DR

This paper characterizes the minimal attached primes of local cohomology modules of binomial edge ideals in block graphs, providing combinatorial insights and an alternative proof leveraging recent related results.

Contribution

It offers a combinatorial characterization of non-vanishing local cohomology modules for binomial edge ideals of block graphs, and presents an alternative proof based on recent work.

Findings

Identified minimal attached primes for these modules

Characterized non-vanishing local cohomology modules combinatorially

Provided an alternative proof using recent results

Abstract

We calculate the minimal attached primes of the local cohomology modules of the binomial edge ideals of block graphs. In particular, we obtain a combinatorial characterisation of which of these modules are non-vanishing. We also show that the main result of this paper follows from a recent result of Lax, Rinaldo, and Romeo (arXiv:2405.08671, Theorem 3.2), which was published independently during the writing of this paper. This provides a short alternative proof of our result.