Generic initial ideals, graded Betti numbers and $k$-Lefschetz properties
| dc.creator | Harima, Tadahito | |
| dc.creator | Wachi, Akihito | |
| dc.date | 2007-07-16 | |
| dc.date | 2007-07-19 | |
| dc.date.accessioned | 2026-07-07T08:18:55Z | |
| dc.date.available | 2026-07-07T08:18:55Z | |
| dc.description | We introduce the $k$-strong Lefschetz property ($k$-SLP) and the $k$-weak Lefschetz property ($k$-WLP) for graded Artinian $K$-algebras, which are generalizations of the Lefschetz properties. The main results obtained in this paper are as follows: 1. Let $I$ be a graded ideal of $R=K[x_1, x_2, x_3]$ whose quotient ring $R/I$ has the SLP. Then the generic initial ideal of $I$ is the unique almost revlex ideal with the same Hilbert function as $R/I$. 2. Let $I$ be a graded ideal of $R=K[x_1, x_2, ..., x_n]$ whose quotient ring $R/I$ has the $n$-SLP. Suppose that all $k$-th differences of the Hilbert function of $R/I$ are quasi-symmetric. Then the generic initial ideal of $I$ is the unique almost revlex ideal with the same Hilbert function as $R/I$. 3. We give a sharp upper bound on the graded Betti numbers of Artinian $K$-algebras with the $k$-WLP and a fixed Hilbert function. | |
| dc.description | 36 pages; a refererence [CP07] added | |
| dc.identifier | https://arxiv.org/abs/0707.2247 | |
| dc.identifier | http://arxiv.org/abs/0707.2247 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/134600 | |
| dc.subject | Commutative Algebra | |
| dc.subject | 13A02 (Primary) 13D07, 13F20, 13D40, 13C05 (Secondary) | |
| dc.title | Generic initial ideals, graded Betti numbers and $k$-Lefschetz properties | |
| dc.type | text |