一类归约数为1的自反向量丛

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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