四次曲线的（正）二次行列式表示和罗宾逊多项式

IF 1.1 3区数学 Q1 MATHEMATICS

Linear Algebra and its Applications Pub Date : 2025-09-08 DOI:10.1016/j.laa.2025.09.006

Clemens Brüser, Mario Kummer

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引用次数: 0

摘要

证明了复零集光滑的实非负三元四次元可以表示为处处为正半定的二次元对称矩阵的行列式。我们证明了罗宾逊多项式的相应陈述不成立，回答了Buckley和Šivic提出的问题。

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(Positive) quadratic determinantal representations of quartic curves and the Robinson polynomial

We prove that every real nonnegative ternary quartic whose complex zero set is smooth can be represented as the determinant of a symmetric matrix with quadratic entries which is everywhere positive semidefinite. We show that the corresponding statement fails for the Robinson polynomial, answering a question by Buckley and Šivic.

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来源期刊

Linear Algebra and its Applications 数学-应用数学

CiteScore

2.20

自引率

9.10%

发文量

333

审稿时长

13.8 months

期刊介绍： Linear Algebra and its Applications publishes articles that contribute new information or new insights to matrix theory and finite dimensional linear algebra in their algebraic, arithmetic, combinatorial, geometric, or numerical aspects. It also publishes articles that give significant applications of matrix theory or linear algebra to other branches of mathematics and to other sciences. Articles that provide new information or perspectives on the historical development of matrix theory and linear algebra are also welcome. Expository articles which can serve as an introduction to a subject for workers in related areas and which bring one to the frontiers of research are encouraged. Reviews of books are published occasionally as are conference reports that provide an historical record of major meetings on matrix theory and linear algebra.