The Multiplicity Conjecture for Barycentric Subdivisions

Details The Multiplicity Conjecture for Barycentric Subdivisions The Multiplicity Conjecture for Barycentric Subdivisions

2006-06-12

arxiv.org/abs/math/0606274v3

Mathematics

Commutative Algebra

28, pages, lower bound and equality cases added

Scientific paper

For a simplicial complex $\Delta$ 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 & 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 $\Delta$ to the one of its barycentric subdivision.

Affiliated with

Also associated with

No associations

Rating

The Multiplicity Conjecture for Barycentric Subdivisions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The Multiplicity Conjecture for Barycentric Subdivisions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Multiplicity Conjecture for Barycentric Subdivisions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-648019