Borel-fixed ideals and reduction number

dc.creatorHoa, Le Tuan
dc.creatorTrung, Ngo Viet
dc.date2003-11-18
dc.date.accessioned2026-07-07T05:03:00Z
dc.date.available2026-07-07T05:03:00Z
dc.descriptionThe 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.description11 pages
dc.identifierhttps://arxiv.org/abs/math/0311300
dc.identifierhttp://arxiv.org/abs/math/0311300
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/69237
dc.subjectCommutative Algebra
dc.subjectAlgebraic Geometry
dc.subject13A02, 13P10
dc.titleBorel-fixed ideals and reduction number
dc.typetext

Files

Collections