2006/06/10 by Isabella Novik, Novik, Isabella, Ed Swartz +1 · 1 citation
Mathematics · #05B35 #13D02 #13F55 #13H15 #52B05 #Advanced Combinatorial Mathematics #Algebraic Geometry and Number Theory #Combinatorics (math.CO) #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.math/0606246
openalex publication_date 2006/06/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 (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 via the Cohen-Macaulay connectivity of the skeletons of the complex.