Corpus ID: 237494726

Comparision between regularity of small symbolic powers and ordinary powers of an edge ideal

@inproceedings{Minh2021ComparisionBR,
  title={Comparision between regularity of small symbolic powers and ordinary powers of an edge ideal},
  author={Nguy{\^e}n C{\^o}ng Minh and Le Dinh Nam and Thieu Dinh Phong and Phan Thi Thu Thuy and Thanh Vu},
  year={2021}
}
Let G be a simple graph and I its edge ideal. We prove that reg(I) = reg(Is) for s = 2, 3, where I is the s-th symbolic power of I. As a consequence, we prove the following bounds reg Is ≤ reg I + 2s− 2, for s = 2, 3, reg I ≤ reg I + 2s− 2, for s = 2, 3, 4. 

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TLDR
This work studies the topology of the lcm-lattice of edge ideals and derives upper bounds on the Castelnuovo-Mumford regularity of the ideals and shows that the second power of the edge ideal has a linear resolution. Expand
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