Type: Article

Higher Jacobian matrix of weighted homogeneous polynomials and derivation algebras

Badilla Céspedes, Wágner; Castorena Abel, Duarte, Daniel;

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.