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arXiv · 1904.07717

Invariants of the symbolic powers of edge ideals

Bidwan Chakraborty·Mousumi Mandal
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Abstract

Let $G$ be a graph and $I=I(G)$ be its edge ideal. When $G$ is the clique sum of two different length odd cycles joined at single vertex then we give an explicit description of the symbolic powers of $I$ and compute the Waldschmidt constant. When $G$ is complete graph then we describe the generators of the symbolic powers of $I$ and compute the Waldschmidt constant and the resurgence of $I$. Moreover for complete graph we prove that the Castelnuvo-Mumford regularity of the symbolic powers and ordinary powers of the edge ideal coincide.

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Bidwan Chakraborty, Mousumi Mandal. 2019-04-16. Invariants of the symbolic powers of edge ideals. https://arxiv.org/abs/1904.07717

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