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

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