On Rees algebras of linearly presented ideals and modules

IF 0.7 2区 数学 Q2 MATHEMATICS
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引用次数: 0

Abstract

Let I be a perfect ideal of height two in \(R=k[x_1, \ldots , x_d]\) and let \(\varphi \) denote its Hilbert–Burch matrix. When \(\varphi \) has linear entries, the algebraic structure of the Rees algebra \({\mathcal {R}}(I)\) is well-understood under the additional assumption that the minimal number of generators of I is bounded locally up to codimension \(d-1\) . In the first part of this article, we determine the defining ideal of \({\mathcal {R}}(I)\) under the weaker assumption that such condition holds only up to codimension \(d-2\) , generalizing previous work of P. H. L. Nguyen. In the second part, we use generic Bourbaki ideals to extend our findings to Rees algebras of linearly presented modules of projective dimension one.

论线性呈现的理想和模块的里斯代数
摘要 让 I 是 \(R=k[x_1, \ldots , x_d]\) 中高为二的完全理想,让 \(\varphi \) 表示它的希尔伯特-伯奇矩阵。当 \(\varphi \)有线性条目时,在 I 的最小生成数是局部有界的(直到编码维度 \(d-1\))这一额外假设下,里斯代数 \({\mathcal {R}}(I)\) 的代数结构是很好理解的。在本文的第一部分中,我们在较弱的假设条件下确定了 \({\mathcal {R}}(I)\) 的定义理想,这个假设条件只在\(d-2\) 的编码维度上成立,概括了 P. H. L. Nguyen 之前的工作。在第二部分中,我们使用泛布尔巴基理想将我们的发现扩展到投影维数为一的线性呈现模块的里斯代数。
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来源期刊
Collectanea Mathematica
Collectanea Mathematica 数学-数学
CiteScore
2.70
自引率
9.10%
发文量
36
审稿时长
>12 weeks
期刊介绍: Collectanea Mathematica publishes original research peer reviewed papers of high quality in all fields of pure and applied mathematics. It is an international journal of the University of Barcelona and the oldest mathematical journal in Spain. It was founded in 1948 by José M. Orts. Previously self-published by the Institut de Matemàtica (IMUB) of the Universitat de Barcelona, as of 2011 it is published by Springer.
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