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Type: Article
Higher Jacobian matrix of weighted homogeneous polynomials and derivation algebras
Abstract:
We prove that the ideal generated by the maximal minors of the higher-order Jacobian matrix of a weighted homogeneous polynomial is also weighted homogeneous. As an application, we give a partial answer to a conjecture concerning the non-existence of negative weight derivations on the higher Nash blowup local algebra of a hypersurface.
We prove that the ideal generated by the maximal minors of the higher-order Jacobian matrix of a weighted homogeneous polynomial is also weighted homogeneous. As an application, we give a partial answer to a conjecture concerning the non-existence of negative weight derivations on the higher Nash blowup local algebra of a hypersurface.
Keywords: Higher Nash blowup local algebras|| Higher-order Jacobian matrix||Weighted homogeneous isolated hypersurface singularities
MSC: 14B05, 32S05, 13N15
Journal: Journal of Singularities
ISSN: 1949-2006
Year: 2025
Volume: 28
Pages: 197-206
Revision: 1
Notas: Q3 (USA) Web of Science. Q3 Scopus. El primer autor recibió apoyo del Programa Posdoctoral de la UNAM (POSDOC). El segundo autor recibió apoyo del proyecto IN100723, “Curvas, Sistemas lineales en superficies proyectivas
y fibrados vectoriales” de la DGAPA, UNAM. El tercer autor cuenta con el apoyo del proyecto CONAHCYT
CF-2023-G-33.
Created: 2025-08-27 15:46:33
Modified: 2025-11-10 16:35:29
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