Linearly presented perfect ideals of codimension 2 in three variables

JOURNAL OF ALGEBRA

卷:512

Article

Doria, Andre¹  Ramos, Zaqueu¹  Simis, Aron² 

[1] Univ Fed Sergipe, Dept Matemat, CCET, BR-49100000 Sao Cristovao, Sergipe, Brazil

[2] Univ Fed Pernambuco, Dept Matemat, CCEN, BR-50740560 Recife, PE, Brazil

关键词: Linear presentation;    Cohen-Macaulay ideal;    Special fiber;    Rees algebra;    Reduction number;   

DOI  :  10.1016/j.jalgebra.2018.06.032

来源: Elsevier

【 摘 要 】

The goal of this paper is the fine structure of the ideals in the title, with emphasis on the properties of the associated Rees algebra and the special fiber. The watershed between the present approach and some of the previous work in the literature is that here one does not assume that the ideals in question satisfy the usual generic properties. One exception is a recent work of N. P. H. Lan which inspired the present work. Here we recover and extend his work. We strongly focus on the behavior of the ideals of minors of the corresponding so-called Hilbert-Burch matrix and on conjugation features of the latter. We apply the results to three important models: linearly presented ideals of plane fat points, reciprocal ideals of hyperplane arrangements and linearly presented monomial ideals. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free