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.

On schemes evinced by generalized additive decompositions and their regularity / Bernardi, Alessandra; Oneto, Alessandro; Taufer, Daniele. - In: JOURNAL DE MATHÉMATIQUES PURES ET APPLIQUÉES. - ISSN 1776-3371. - 2024, 188:(2024), pp. 446-469. [10.1016/j.matpur.2024.06.007]

On schemes evinced by generalized additive decompositions and their regularity

Bernardi, Alessandra;Oneto, Alessandro;Taufer, Daniele
2024-01-01

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.
2024
Bernardi, Alessandra; Oneto, Alessandro; Taufer, Daniele
On schemes evinced by generalized additive decompositions and their regularity / Bernardi, Alessandra; Oneto, Alessandro; Taufer, Daniele. - In: JOURNAL DE MATHÉMATIQUES PURES ET APPLIQUÉES. - ISSN 1776-3371. - 2024, 188:(2024), pp. 446-469. [10.1016/j.matpur.2024.06.007]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/417091
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