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Face Ring Multiplicity via CM-Connectivity Sequences

Published online by Cambridge University Press:  20 November 2018

Isabella Novik  and
Ed Swartz
Isabella Novik
Affiliation:
Department of Mathematics, University of Washington, Seattle, WA 98195-4350, USA, e-mail:novik@math.washington.edu
Ed Swartz
Affiliation:
Department of Mathematics, University of Washington, Seattle, WA 98195-4350, USA, e-mail:novik@math.washington.edu
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Abstract

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The multiplicity conjecture of Herzog, Huneke, and Srinivasan is verified for the face rings of the following classes of simplicial complexes: matroid complexes, complexes of dimension one and two, and Gorenstein complexes of dimension at most four. The lower bound part of this conjecture is also established for the face rings of all doubly Cohen–Macaulay complexes whose 1-skeleton's connectivity does not exceed the codimension plus one as well as for all $\text{(}d-1)$-dimensional $d$-Cohen–Macaulay complexes. The main ingredient of the proofs is a new interpretation of the minimal shifts in the resolution of the face ring $\mathbf{k}[\Delta ]$ via the Cohen–Macaulay connectivity of the skeletons of $\Delta $.

Keywords

13F5552B0513H1513D0205B35
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 61 , Issue 4 , 01 August 2009 , pp. 888 - 903
Copyright
Copyright © Canadian Mathematical Society 2012

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