The Multiplicity Conjecture for Barycentric Subdivisions
Titel:
The Multiplicity Conjecture for Barycentric Subdivisions
Auteur:
Kubitzke, Martina Welker, Volkmar
Verschenen in:
Communications in algebra
Paginering:
Jaargang 36 (2008) nr. 11 pagina's 4223-4248
Jaar:
2008-11
Inhoud:
For a simplicial complex Δ we study the effect of barycentric subdivision on ring theoretic invariants of its Stanley-Reisner ring. In particular, for Stanley-Reisner rings of barycentric subdivisions we verify a conjecture by Huneke and Herzog and Srinivasan, that relates the multiplicity of a standard graded k-algebra to the product of the maximal and minimal shifts in its minimal free resolution up to the height. On the way to proving the conjecture, we develop new and list well-known results on behavior of dimension, Hilbert series, multiplicity, local cohomology, depth, and regularity when passing from the Stanley-Reisner ring of Δ to the one of its barycentric subdivision.
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