On the containment problem

By Tomasz Szemberg, Justyna Szpond. 2016

48 citations recorded by the source corpus.

The purpose of this note is to provide an overview of the containment problem for symbolic and ordinary powers of homogeneous ideals, related conjectures and examples. We focus here on ideals with zero dimensional support. This is an area of ongoing active research. We conclude the note with a list of potential promising paths of further research.

Subfields: Algebra and Number Theory, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/7eb11a061928e8edbec6d82c8f66042a77877eca

How researchers see this paper

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In Algebra and Number Theory

1. Luis N'unez-Betancourt
2. Hailong Dao
3. A. Stefani
4. Eloísa Grifo
5. Craig Huneke
6. Juan Migliore
7. Brian Harbourne
8. R. Mir'o-Roig

In Computational Theory and Mathematics

1. Luis N'unez-Betancourt
2. Hailong Dao
3. Craig Huneke

Citations in the corpus

• Symbolic Powers of Ideals (2015, background): “.22 (Harbourne). Given a radical homogeneous ideal Iin k[PN], let hbe the maximal height of an associated prime of I. Then for all n> 1, I(hn−h+1) ⊆ In. For a survey on the containment problem see [SS16]. Harbourne and Bocci introduced the resurgence of an ideal as an asymptotic measure of the be”