一类归约数为1的自反向量丛

IF 0.3 4区数学 Q4 MATHEMATICS

Mathematica Scandinavica Pub Date : 2019-06-17 DOI:10.7146/MATH.SCAND.A-111889

Cleto B. Miranda-Neto

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引用次数: 1

摘要

现代交换代数中的一个难题要求给出具有规定约简数$r\geq 1$的模块(更有趣的是，自反向量束)的例子。如果我们对里斯代数的良好性质感兴趣，问题就更微妙了。在本文中，我们考虑$r=1$的情况。准确地说，我们证明了射影$3$ -空间中任意次费马因子的对数向量场模是一个约简数$1$和Gorenstein Rees环的自反向量束。

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A family of reflexive vector bundles of reduction number one

A difficult issue in modern commutative algebra asks for examples of modules (more interestingly, reflexive vector bundles) having prescribed reduction number $r\geq 1$. The problem is even subtler if in addition we are interested in good properties for the Rees algebra. In this note we consider the case $r=1$. Precisely, we show that the module of logarithmic vector fields of the Fermat divisor of any degree in projective $3$-space is a reflexive vector bundle of reduction number $1$ and Gorenstein Rees ring.

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来源期刊

Mathematica Scandinavica 数学-数学

CiteScore

0.60

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Mathematica Scandinavica is a peer-reviewed journal in mathematics that has been published regularly since 1953. Mathematica Scandinavica is run on a non-profit basis by the five mathematical societies in Scandinavia. It is the aim of the journal to publish high quality mathematical articles of moderate length. Mathematica Scandinavica publishes about 640 pages per year. For 2020, these will be published as one volume consisting of 3 issues (of 160, 240 and 240 pages, respectively), enabling a slight increase in article pages compared to previous years. The journal aims to publish the first issue by the end of March. Subsequent issues will follow at intervals of approximately 4 months. All back volumes are available in paper and online from 1953. There is free access to online articles more than five years old.