Ordinary and symbolic powers of edge ideals of weighted oriented graphs

Abstract

Let $\mathcal{D}$ be a weighted oriented graph and $I(\mathcal{D})$ be its edge ideal. In this paper, we show that all the symbolic and ordinary powers of $I(\mathcal{D})$ coincide when $\mathcal{D}$ is a weighted oriented certain class of tree. Finally, we give necessary and sufficient conditions for the equality of ordinary and symbolic powers of naturally oriented lines.

arXiv comment7 pages

References in corpus (1)

• Comparing symbolic powers of edge ideals of weighted oriented graphs

Cited by in corpus (1)

• Normally torsion-free edge ideals of weighted oriented graphs