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.

中文翻译：

---

二项式边缘理想及其一般初始理想的局部同调

我们为二项式边理想的局部同调模块提供了一个Hochster型公式。结果，我们获得了这些理想的Cohen-Macaulayness和Buchsbaumness的简单准则，并描述了它们的Castelnuovo-Mumford正则性及其希尔伯特级数。Conca和Varbaro（无方Groebner变性，2018）最近证明了Conca，De Negri和Gorla（J Comb代数2：231–257，2018）的猜想，涉及到Cartwright–Sturmfels理想的局部同调模块的等级成分及其最初的理想。我们为二项式边缘理想的情况提供了另一种证明。