Local cohomology of binomial edge ideals and their generic ideals

TL;DR

This paper develops a Hochster type formula for local cohomology of binomial edge ideals, providing criteria for Cohen-Macaulayness and insights into their algebraic invariants, while confirming a related conjecture.

Contribution

It introduces a Hochster type formula for local cohomology of binomial edge ideals and proves a conjecture relating their local cohomology to generic initial ideals.

Findings

Hochster type formula for local cohomology modules

Criterion for Cohen-Macaulayness of binomial edge ideals

Verification of a conjecture relating local cohomology and generic initial ideals

Abstract

We provide a Hochster type formula for the local cohomology modules of binomial edge ideals. As a consequence we obtain a simple criterion for the Cohen-Macaulayness of these ideals and we describe their Castelnuovo-Mumford regularity and their Hilbert series. We also prove a conjecture of Conca, De Negri and Gorla relating the graded components of the local cohomology modules of binomial edge ideals and their generic initial ideals.