Conditions for Generic Initial Ideals to be Almost Reverse Lexicographic
| dc.creator | Cho, Young Hyun | |
| dc.creator | Park, Jung Pil | |
| dc.date | 2007-07-10 | |
| dc.date | 2007-07-16 | |
| dc.date.accessioned | 2026-07-07T08:17:29Z | |
| dc.date.available | 2026-07-07T08:17:29Z | |
| dc.description | 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 Fröberg 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 Fröberg conjecture. | |
| dc.description | 10 pages | |
| dc.identifier | https://arxiv.org/abs/0707.1365 | |
| dc.identifier | http://arxiv.org/abs/0707.1365 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/134109 | |
| dc.subject | Commutative Algebra | |
| dc.subject | 13A02; 13C05; 13D40; 13E10; 13P10 | |
| dc.title | Conditions for Generic Initial Ideals to be Almost Reverse Lexicographic | |
| dc.type | text |