Waring identifiability for powers of forms via degenerations

IF 1.5 1区数学 Q1 MATHEMATICS

Proceedings of the London Mathematical Society Pub Date : 2023-12-19 DOI:10.1112/plms.12579

Alex Casarotti, Elisa Postinghel

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引用次数: 0

Abstract

We discuss an approach to the secant non-defectivity of the varieties parametrising

k $k$

th powers of forms of degree

d $d$

. It employs a Terracini-type argument along with certain degeneration arguments, some of which are based on toric geometry. This implies a result on the identifiability of the Waring decompositions of general forms of degree kd as a sum of

k $k$

th powers of degree

d $d$

forms, for which an upper bound on the Waring rank was proposed by Fröberg, Ottaviani and Shapiro.

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通过退化实现形式幂的瓦林可识别性

我们讨论的是参数化 k$k$th 阶幂的 d$d$ 形式的secant 非缺陷性的方法。它采用了特拉奇尼型论证和某些退化论证，其中一些论证是基于环几何的。这意味着关于度数为 kd 的一般形式的瓦林分解作为度数为 dd 的形式的 k$k$th 次幂之和的可识别性的结果，弗洛伯格、奥塔维亚尼和夏皮罗为此提出了瓦林等级的上限。

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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来源期刊

Proceedings of the London Mathematical Society 数学-数学

CiteScore

2.90

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： The Proceedings of the London Mathematical Society is the flagship journal of the LMS. It publishes articles of the highest quality and significance across a broad range of mathematics. There are no page length restrictions for submitted papers. The Proceedings has its own Editorial Board separate from that of the Journal, Bulletin and Transactions of the LMS.