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| Paper IPM / M / 16951 |
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| Abstract: | |
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Let G be a graph on the vertex set [n] and JG the associated binomial edge ideal in the polynomial ring S=\KK[x1,…,xn,y1,…,yn]. In this paper we investigate the depth of binomial edge ideals. More precisely, we first establish a combinatorial lower bound for the depth of S/JG based on some graphical invariants of G. Next, we combinatorially characterize all binomial edge ideals JG with \depth S/JG=5. To achieve this goal, we associate a new poset MG with the binomial edge ideal of G, and then elaborate some topological properties of certain subposets of MG in order to compute some local cohomology modules of S/JG.
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