Borel-fixed ideals and reduction number
| dc.creator | Hoa, Le Tuan | |
| dc.creator | Trung, Ngo Viet | |
| dc.date | 2003-11-18 | |
| dc.date.accessioned | 2026-07-07T05:03:00Z | |
| dc.date.available | 2026-07-07T05:03:00Z | |
| dc.description | The aim of this paper is to study the relationship between reduction numbers and Borel-fixed ideals in all characteristics. By definition, Borel-fixed ideals are closed under certain specializations which is similar to the strong stability. We will estimate the number of monomials which can be specialized to a given monomial. As a consequence, we obtain a combinatorial version of the well-known Eakin-Sathaye's theorem which bounds the reduction number in terms of the Hilbert function. Furthermore, we show that the bound of Eakin-Sathaye's theorem is attained by the reduction number of a lex-segment monomial ideal. This result answers a question of Conca in the affirmative. We will also show that the reduction number of the lex-segment ideal is bounded exponentially by the reduction number of the given ideal. | |
| dc.description | 11 pages | |
| dc.identifier | https://arxiv.org/abs/math/0311300 | |
| dc.identifier | http://arxiv.org/abs/math/0311300 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/69237 | |
| dc.subject | Commutative Algebra | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 13A02, 13P10 | |
| dc.title | Borel-fixed ideals and reduction number | |
| dc.type | text |