An elementary approach to containment relations between symbolic and ordinary powers of certain monomial ideals

ABSTRACT

We provide an elementary explanation of a surprising result of Ein–Lazarsfeld–Smith and Hochster–Huneke on the containment between symbolic and ordinary powers of ideals for a certain class of simple monomial ideals.

KEYWORDS:

• Monomial ideals
• symbolic powers

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 14C99
• 13C05

Acknowledgements

This work is the result of an ‘Elective Undergraduate Research’ class at the Budapest Semesters in Mathematics in Spring 2014. After our proofs were completed, Brian Harbourne and Tomasz Szemberg have pointed out closely related work in the area (see Remark 2.8, Remark 2.9, and Remark 2.10, respectively, for more precise statements and references) for which we are grateful.