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

Abstract

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 ${\Delta }^{\prime }$. In particular, we show that the arithmetical rank of the Stanley-Reisner ideal of ${\Delta }^{\prime }$ equals the projective dimension of the Stanley-Reisner ring of ${\Delta }^{\prime }$ if the corresponding equality holds for $\Delta$.

References in corpus (3)

• A note on the edge ideals of Ferrers graphs
• On the arithmetical rank of certain monomial ideals
• On the arithmetical rank of the edge ideals of forests

Cited by in corpus (1)

• The Stanley-Reisner ideals of polygons as set-theoretic complete intersections