Differences in regularities of a power and its integral closure and symbolic power

Abstract

We show that for a square-free monomial ideal, the regularity of its symbolic (second) power and of the integral closure of of its (second) power can differ from the regularity of its ordinary (second) power by an arbitrarily large integer.

Keywords:

• Monomial ideals
• splitting

2020 Mathematics Subject Classification:

• Primary: 13H10
• 13F55
• Secondary: 05E40
• 05E45

Acknowledgments

The computational commutative algebra package Macaulay2 [1] was heavily used to compute several examples.