The module of logarithmic derivations of a generic determinantal ideal,Proceedings of the American Mathematical Society

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The module of logarithmic derivations of a generic determinantal ideal
Proceedings of the American Mathematical Society ( IF 0.8 ) Pub Date : 2020-08-11 , DOI: 10.1090/proc/15142
Ricardo Burity , Cleto B. Miranda-Neto

Abstract:An important problem in algebra and related fields (such as algebraic and complex analytic geometry) is to find an explicit, well-structured, minimal set of generators for the module of logarithmic derivations of classes of homogeneous ideals in polynomial rings. In this note we settle the case of the ideal $P\subset R=K[\{X_{i,j}\}]$ generated by the maximal minors of an $(n+1)\times n$ generic matrix $(X_{i,j})$ over an arbitrary field

with $n\geq 2$ . We also characterize when the derivation module of

is Ulrich, and we investigate this property if we replace

by determinantal rings arising from simple degenerations of the generic case.

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中文翻译：

一般行列式理想的对数导数模块

摘要：代数和相关领域（例如代数和复杂解析几何）的一个重要问题是为多项式环中齐次理想类的对数导数模块找到一个显式，结构良好的最小生成器集。在这份说明中，我们解决理想的情况下通过的最大的未成年人产生的通用矩阵任意域上使用。我们还表征了何时的推导模块为Ulrich，并且如果我们替换为由普通情况的简单退化引起的行列式环，则我们将研究此属性。 $P \ subset R = K [\ {X_ {i，j} \}]$ $（n + 1）\次n$ $（X_ {i，j}）$

$n \ geq 2$

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更新日期：2020-09-02

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