Symbolic Powers of Monomial Ideals

By Susan M. Cooper, Robert J. D. Embree, Huy Tài Hà, Andrew H. Hoefel. Proceedings of the Edinburgh Mathematical Society, 2013

82 citations recorded by the source corpus.

Abstract We investigate symbolic and regular powers of monomial ideals. For a square-free monomial ideal I ⊆ 𝕜[x 0, … , xn ] we show that for all positive integers m, t and r, where e is the big-height of I and . This captures two conjectures (r = 1 and r = e): one of Harbourne and Huneke, and one of Bocci et al. We also introduce the symbolic polyhedron of a monomial ideal and use this to explore symbolic powers of non-square-free monomial ideals.

Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/4d509718613cb0413147fa5efbdb3c63bf749502

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Citations in the corpus

The Waldschmidt constant for squarefree monomial ideals (2015, methodology): “The Waldschmidt constant of monomial ideals (not just squarefree) was first studied in [6] (although some special cases can be found in [2, 14]) which formulates the computation of α̂(I) as a minimal value problem on a polyhedron constructed from the generators of I.”
On the containment problem (2016, background): “Since then, a number of further counterexamples has been constructed [2, 9, 4, 11].”