Componentwise linear symbolic powers of edge ideals and Minh's conjecture
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866915024591650816 |
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| author | Ficarra, Antonino Moradi, Somayeh Römer, Tim |
| author_facet | Ficarra, Antonino Moradi, Somayeh Römer, Tim |
| contents | 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 $G$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_11537 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Componentwise linear symbolic powers of edge ideals and Minh's conjecture Ficarra, Antonino Moradi, Somayeh Römer, Tim Commutative Algebra Combinatorics 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 $G$. |
| title | Componentwise linear symbolic powers of edge ideals and Minh's conjecture |
| topic | Commutative Algebra Combinatorics |
| url | https://arxiv.org/abs/2411.11537 |