Arithmetical ranks of Stanley-Reisner ideals of simplicial complexes with a cone

Details Arithmetical ranks of Stanley-Reisner ideals of simplicial complexes with a cone Arithmetical ranks of Stanley-Reisner ideals of simplicial complexes with a cone

2008-09-12

arxiv.org/abs/0809.2194v1

Mathematics

Commutative Algebra

Scientific paper

When a cone is added to a simplicial complex $\Delta$ over one of its faces, we investigate the relation between the arithmetical ranks of the Stanley-Reisner ideals of the original simplicial complex and the new simplicial complex $\Delta'$. In particular, we show that the arithmetical rank of the Stanley-Reisner ideal of $\Delta'$ equals the projective dimension of the Stanley-Reisner ring of $\Delta'$ if the corresponding equality holds for $\Delta$.

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