




















Abstract:We study local generalized additive decompositions (GADs) of homogeneous polynomials and their associated points schemes through their local inverse systems. We verify that their construction and algebraic properties are independent of the chosen apolarity action. We propose a determinantal method for computing minimal local GADs by minimizing the rank of a symbolic inverse system. When the locus of minimal supports is finite, this procedure provides a practical tool to determine all minimal local decompositions without tensor extensions. We prove that this finiteness is guaranteed whenever the local GAD-rank of the form does not exceed its degree. We analyze both generic and special cases, provide computational evidence assessing the impact of different choices for minors in the determinantal algorithm, and compare our approach with existing algorithms for local apolar schemes.
From: Daniele Taufer [view email]
[v1]
Mon, 9 Mar 2026 18:47:17 UTC (24 KB)
[v2]
Tue, 16 Jun 2026 15:24:34 UTC (29 KB)
此内容由惯性聚合(RSS阅读器)自动聚合整理,仅供阅读参考。 原文来自 — 版权归原作者所有。