The Hilbert functions which force the Weak Lefschetz Property

Details The Hilbert functions which force the Weak Lefschetz Property The Hilbert functions which force the Weak Lefschetz Property

2006-09-05

arxiv.org/abs/math/0609150v2

JPAA 210 (2007), No. 2, 465-471

Mathematics

Commutative Algebra

A few minor changes. To appear in JPAA

Scientific paper

The purpose of this note is to characterize the finite Hilbert functions which force all of their artinian algebras to enjoy the Weak Lefschetz Property (WLP). Curiously, they turn out to be exactly those (characterized by Wiebe in $[Wi]$) whose Gotzmann ideals have the WLP. This implies that, if a Gotzmann ideal has the WLP, then all algebras with the same Hilbert function (and hence lower Betti numbers) have the WLP as well. However, we will answer in the negative, even in the case of level algebras, the most natural question that one might ask after reading the previous sentence: If $A$ is an artinian algebra enjoying the WLP, do all artinian algebras with the same Hilbert function as $A$ and Betti numbers lower than those of $A$ have the WLP as well? Also, as a consequence of our result, we have another (simpler) proof of the fact that all codimension 2 algebras enjoy the WLP (this fact was first proven in $[HMNW]$, where it was shown that even the Strong Lefschetz Property holds).

Affiliated with

Also associated with

No associations

Rating

The Hilbert functions which force the Weak Lefschetz Property 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 Hilbert functions which force the Weak Lefschetz Property, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Hilbert functions which force the Weak Lefschetz Property will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-555000