Symbolic powers of edge ideals of graphs
Abstract
Let $G$ be a graph and let $I = I(G)$ be its edge ideal. When $G$ is unicyclic, we give a decomposition of symbolic powers of $I$ in terms of its ordinary powers. This allows us to explicitly compute the Waldschmidt constant and the resurgence number of $I$. When $G$ is an odd cycle, we explicitly compute the regularity of $I^{(s)}$ for all $s \in \mathbb{N}$. In doing so, we also give a natural lower bound for the regularity function $\text{reg } I^{(s)}$, for $s \in \mathbb{N}$, for an arbitrary graph $G$.
 Publication:

arXiv eprints
 Pub Date:
 May 2018
 arXiv:
 arXiv:1805.03428
 Bibcode:
 2018arXiv180503428G
 Keywords:

 Mathematics  Commutative Algebra;
 13D02;
 13F55;
 13P20
 EPrint:
 19 pages