Toric Initial Ideals of $Δ$-Normal Configurations: Cohen-Macaulayness and Degree Bounds
| dc.creator | O'Shea, Edwin | |
| dc.creator | Thomas, Rekha R. | |
| dc.date | 2003-08-12 | |
| dc.date.accessioned | 2026-07-07T05:00:20Z | |
| dc.date.available | 2026-07-07T05:00:20Z | |
| dc.description | A normal (respectively, graded normal) vector configuration $A$ defines the toric ideal $I_A$ of a normal (respectively, projectively normal) toric variety. These ideals are Cohen-Macaulay, and when $A$ is normal and graded, $I_A$ is generated in degree at most the dimension of $I_A$. Based on this, Sturmfels asked if these properties extend to initial ideals -- when $A$ is normal, is there an initial ideal of $I_A$ that is Cohen-Macaulay, and when $A$ is normal and graded, does $I_A$ have a Gröbner basis generated in degree at most $dim(I_A)$ ? In this paper, we answer both questions positively for $Δ$-normal configurations. These are normal configurations that admit a regular triangulation $Δ$ with the property that the subconfiguration in each cell of the triangulation is again normal. Such configurations properly contain among them all vector configurations that admit a regular unimodular triangulation. We construct non-trivial families of both $Δ$-normal and non-$Δ$-normal configurations. | |
| dc.description | 18 pages, 2 figures | |
| dc.identifier | https://arxiv.org/abs/math/0308109 | |
| dc.identifier | http://arxiv.org/abs/math/0308109 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/68298 | |
| dc.subject | Commutative Algebra | |
| dc.subject | Combinatorics | |
| dc.subject | 13P02, 05E02 | |
| dc.title | Toric Initial Ideals of $Δ$-Normal Configurations: Cohen-Macaulayness and Degree Bounds | |
| dc.type | text |