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arXiv · 0802.1282

On the multiplicity conjecture for non-Cohen-Macaulay simplicial complexes

Michael Goff
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Abstract

We prove a reformulation of the multiplicity upper bound conjecture and use that reformulation to prove it for three-dimensional simplicial complexes and homology manifolds with many vertices. We provide necessary conditions for a Cohen-Macaulay complex with many vertices to have a pure minimal free resolution and a characterization of flag complexes whose minimal free resolution is pure.

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Michael Goff. 2008-02-09. On the multiplicity conjecture for non-Cohen-Macaulay simplicial complexes. https://arxiv.org/abs/0802.1282

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