Comparision between regularity of small symbolic powers and ordinary powers of an edge ideal
Abstract
Let $G$ be a simple graph and $I$ its edge ideal. We prove that $${\rm reg}(I^{(s)}) = {\rm reg}(I^s)$$ for $s = 2,3$, where $I^{(s)}$ is the $s$-th symbolic power of $I$. As a consequence, we prove the following bounds \begin{align*} {\rm reg} I^{s} & \le {\rm reg} I + 2s - 2, \text{ for } s = 2,3, {\rm reg} I^{(s)} & \le {\rm reg} I + 2s - 2,\text{ for } s = 2,3,4. \end{align*}
- Publication:
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arXiv e-prints
- Pub Date:
- September 2021
- DOI:
- 10.48550/arXiv.2109.05242
- arXiv:
- arXiv:2109.05242
- Bibcode:
- 2021arXiv210905242C
- Keywords:
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- Mathematics - Commutative Algebra
- E-Print:
- 24 pages, submitted