Equality of ordinary and symbolic powers of Stanley-Reisner ideals

Details Equality of ordinary and symbolic powers of Stanley-Reisner ideals Equality of ordinary and symbolic powers of Stanley-Reisner ideals

2010-09-04

arxiv.org/abs/1009.0828v1

Mathematics

Commutative Algebra

19 pages

Scientific paper

This paper studies properties of simplicial complexes for which the m-th symbolic power of the Stanley-Reisner ideal equals to the m-th ordinary power for a given m > 1. The main results are combinatorial characterizations of such complexes in the two-dimensional case. It turns out that there exist only a finite number of complexes with this property and that these complexes can be described completely. As a consequence we are able to determine all complexes for which the m-th ordinary power of the Stanley-Reisner ideal is Cohen-Macaulay for a given m > 1.

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