Higher Jacobian matrix of weighted homogeneous polynomials and derivation algebras
Wágner Badilla-Céspedes, Abel Castorena, and Daniel Duarte
Journal of Singularities
volume 28 (2025), 197-206
Received: 1 May 2025.
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.
2020 Mathematical Subject Classification:
14B05, 32S05, 13N15
Key words and phrases:
Higher Nash blowup local algebras, higher-order Jacobian matrix, weighted homogeneous isolated hypersurface singularities
Author(s) information:
Wágner Badilla-Céspedes
Centro de Ciencias Matemáticas
UNAM, Campus Morelia
Morelia, Michoacán, México
email: wagner@matmor.unam.mx
Abel Castorena
Centro de Ciencias Matemáticas
UNAM, Campus Morelia
Morelia, Michoacán, México
email: abel@matmor.unam.mx
Daniel Duarte
Centro de Ciencias Matemáticas
UNAM, Campus Morelia
Morelia, Michoacán, México
email: adduarte@matmor.unam.mx