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arXiv · 2411.11537

Componentwise linear symbolic powers of edge ideals and Minh's conjecture

Antonino Ficarra·Somayeh Moradi·Tim Römer
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Abstract

In this paper, we study the componentwise linearity of symbolic powers of edge ideals. We propose the conjecture that all symbolic powers of the edge ideal of a cochordal graph are componentwise linear. This conjecture is verified for some families of cochordal graphs, including complements of block graphs and complements of proper interval graphs. As a corollary, Minh's conjecture is established for such families. Moreover, we show that $I(G)^{(2)}$ is componentwise linear, for any cochordal graph $G$.

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Antonino Ficarra, Somayeh Moradi, Tim Römer. 2024-11-18. Componentwise linear symbolic powers of edge ideals and Minh's conjecture. https://arxiv.org/abs/2411.11537

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