Papers › On schemes evinced by generalized additive decompositions and their regularity
On schemes evinced by generalized additive decompositions and their regularity
Alessandra Bernardi, Alessandro Oneto, Daniele Taufer
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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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