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

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

2008-02-09

arxiv.org/abs/0802.1282v1

Mathematics

Commutative Algebra

Scientific paper

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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