Borel-fixed ideals and reduction number
摘要
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.
引用
@article{arxiv.math/0311300,
title = {Borel-fixed ideals and reduction number},
author = {Le Tuan Hoa and Ngo Viet Trung},
journal= {arXiv preprint arXiv:math/0311300},
year = {2007}
}
备注
11 pages