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

2021/09/11 by Minh, Nguyen Cong, Nam, Le Dinh, Phong, Thieu Dinh +2
#Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.2109.05242

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 \rm reg I^s amp; ≤ \rm reg I + 2s - 2, for s = 2,3, \rm reg I^(s) amp; ≤ \rm reg I + 2s - 2, for s = 2,3,4.

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