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arXiv · 2309.12961

On schemes evinced by generalized additive decompositions and their regularity

Alessandra Bernardi·Alessandro Oneto·Daniele Taufer
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Abstract

We define and explicitly construct schemes evinced by generalized additive decompositions (GADs) of a given $d$-homogeneous polynomial $F$. We employ GADs to investigate the regularity of $0$-dimensional schemes apolar to $F$, focusing on those satisfying some minimality conditions. We show that irredundant schemes to $F$ need not be $d$-regular, unless they are evinced by special GADs of $F$. Instead, we prove that tangential decompositions of minimal length are always $d$-regular, as well as irredundant apolar schemes of length at most $2d+1$.

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Alessandra Bernardi, Alessandro Oneto, Daniele Taufer. 2023-09-22. On schemes evinced by generalized additive decompositions and their regularity. https://doi.org/10.1016/j.matpur.2024.06.007

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