线束的强度

Pub Date : 2020-04-03 DOI:10.7146/math.scand.a-128529

E. Ballico, Emanuele Ventura

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引用次数: 7

摘要

我们在一个代数变量上引入线束截面的强度。这概括了齐次多项式的强度，齐次多项式最近被引入来解决Stillman猜想，这是交换代数中的一个重要问题。我们建立了这个概念的第一个性质，并给出了在这个框架下求强度上界的一些工具。此外，我们还给出了一些关于通常强度的结果，如强度两个齐次多项式集合的可约性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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The strength for line bundles

We introduce the strength for sections of a line bundle on an algebraic variety. This generalizes the strength of homogeneous polynomials that has been recently introduced to resolve Stillman's conjecture, an important problem in commutative algebra. We establish the first properties of this notion and give some tool to obtain upper bounds on the strength in this framework. Moreover, we show some results on the usual strength such as the reducibility of the set of strength two homogeneous polynomials.

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