A partitioning and related properties for the quotient complex Δ(Blm)/Sl Sm

  • Hersh P
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We study the quotient complex Δ(Blm)/Sl Sm as a means of deducing facts about the ring k[x1,...,xlm]SlSm. It is shown in Hersh (preprint, 2000) that Δ(Blm)/Sl Sm is shellable when l=2, implying Cohen-Macaulayness of k[x1,...,x2m]S2Sm for any field k. We now confirm for all pairs (l,m) with l > 2 and m > 1 that Δ(Blm)/Sl Sm is not Cohen-Macaulay over ℤ/2ℤ, but it is Cohen-Macaulay over fields of characteristic p > m (independent of l). This yields corresponding characteristic-dependent results for k[x1,...,xlm]Sl Sm . We also prove that Δ(Blm)/Sl Sm and the links of many of its faces are collapsible, and we give a partitioning for Δ(Blm)/Sl Sm. © 2002 Elsevier Science B.V. All rights reserved.

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  • Patricia Hersh

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