Local cohomology of binomial edge ideals and their 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 and Buchsbaumness of these ideals and we describe their Castelnuovo–Mumford regularity and their Hilbert series. Conca and Varbaro (Square-free Groebner degenerations, 2018) have recently proved a conjecture of Conca, De Negri and Gorla (J Comb Algebra 2:231–257, 2018) relating the graded components of the local cohomology modules of Cartwright–Sturmfels ideals and their generic initial ideals. We provide an alternative proof for the case of binomial edge ideals.