Characteristic-independence of Betti numbers of graph ideals

Details Characteristic-independence of Betti numbers of graph ideals Characteristic-independence of Betti numbers of graph ideals

2004-08-02

arxiv.org/abs/math/0408016v2

Mathematics

Commutative Algebra

Scientific paper

In this paper we study the Betti numbers of Stanley-Reisner ideals generated in degree 2. We show that the first six Betti numbers do not depend on the characteristic of the ground field. We also show that, if the number of variables $n$ is at most 10, all Betti numbers are independent of the ground field. For $n=11$, there exists precisely 4 examples in which the Betti numbers depend on the ground field. This is equivalent to the statement that the homology of flag complexes with at most 10 vertices is torsion free and that there exists precisely 4 non-isomorphic flag complexes with 11 vertices whose homology has torsion. In each of the 4 examples mentioned above the 8th Betti numbers depend on the ground field and so we conclude that the highest Betti number which is always independent of the ground field is either 6 or 7; if the former is true then we show that there must exist a graph with 12 vertices whose 7th Betti number depends on the ground field.

Affiliated with

Also associated with

No associations

Rating

Characteristic-independence of Betti numbers of graph ideals 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 Characteristic-independence of Betti numbers of graph ideals, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Characteristic-independence of Betti numbers of graph ideals will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-299687