The residuals of lex plus powers ideals and the Eisenbud-Green-Harris conjecture
| dc.creator | Richert, Benjamin P. | |
| dc.creator | Sabourin, Sindi | |
| dc.date | 2005-08-17 | |
| dc.date.accessioned | 2026-07-07T05:22:27Z | |
| dc.date.available | 2026-07-07T05:22:27Z | |
| dc.description | The $n$-type vectors introduced by Geramita, Harima and Shin are in 1-1 correspondence with the Hilbert functions Artinian of lex ideals. Letting $\mathbb{A} =\{a_1,..., a_n\}$ define the degrees of a regular sequence, we construct ${\rm lpp}_{\le\mathbb{A}}$-vectors which are in 1-1 correspondence with the Hilbert functions of certain lex plus powers ideals (depending on $\mathbb{A}$). This construction enables us to show that the residual of a lex plus powers ideal in an appropriate regular sequence is again a lex plus powers ideal. We then use this result to show that the Eisenbud-Green-Harris conjecture is equivalent to showing that lex plus powers ideals have the largest last graded Betti numbers (it is well-known that the Eisenbud-Green-Harris conjecture is equivalent to showing that lex plus powers ideals have the largest first graded Betti numbers). | |
| dc.description | 32 pages | |
| dc.identifier | https://arxiv.org/abs/math/0508334 | |
| dc.identifier | http://arxiv.org/abs/math/0508334 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/76068 | |
| dc.subject | Commutative Algebra | |
| dc.subject | 13F20 (Primary) 13D02, 13D40 (Secondary) | |
| dc.title | The residuals of lex plus powers ideals and the Eisenbud-Green-Harris conjecture | |
| dc.type | text |