Conditions for Generic Initial Ideals to be Almost Reverse Lexicographic

Details Conditions for Generic Initial Ideals to be Almost Reverse Lexicographic Conditions for Generic Initial Ideals to be Almost Reverse Lexicographic

2007-07-10

arxiv.org/abs/0707.1365v2

Mathematics

Commutative Algebra

10 pages

Scientific paper

Let $I$ be a homogeneous Artinian ideal in a polynomial ring $R=k[x_1,...,x_n]$ over a field $k$ of characteristic 0. We study an equivalent condition for the generic initial ideal $\gin(I)$ with respect to reverse lexicographic order to be almost reverse lexicographic. As a result, we show that Moreno-Socias conjecture implies Fr\"{o}berg conjecture. And for the case $\Codim I \le 3$, we show that $R/I$ has the strong Lefschetz property if and only if $\gin(I)$ is almost reverse lexicographic. Finally for a monomial complete intersection Artinian ideal $I=(x_1^{d_1},...,x_n^{d_n})$, we prove that $\gin(I)$ is almost reverse lexicographic if $d_i > \sum_{j=1}^{i-1} d_j - i + 1$ for each $i \ge 4$. Using this, we give a positive partial answer to Moreno-Socias conjecture, and to Fr\"{o}berg conjecture.

Affiliated with

Also associated with

No associations

Rating

Conditions for Generic Initial Ideals to be Almost Reverse Lexicographic 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 Conditions for Generic Initial Ideals to be Almost Reverse Lexicographic, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Conditions for Generic Initial Ideals to be Almost Reverse Lexicographic will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-453348