Non-existence of negative derivations on the higher Nash blowup local algebra

2025/08/20 by Badilla-Céspedes, Wágner, Castorena, Abel, Duarte, Daniel +1
#Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.2508.14353

Abstract

Let f∈ℂ[x₁,…,x_s] be a weighted homogeneous polynomial having an isolated singularity and T_n(f) be its higher Nash blowup local algebra. We show that T_n(f) does not admit negative weighted derivations for n≥2. This answers affirmatively a conjecture of Hussain-Ma-Yau-Zuo.

Citations

• Higher Jacobian matrix of weighted homogeneous polynomials and derivation algebras
• Higher Jacobian ideals, contact equivalence and motivic zeta functions
• On the k-torsion of the module of differentials of order n of\n hypersurfaces
• Quantifying singularities with differential operators
• On the module of differentials of order n of hypersurfaces

Related

• Higher Jacobian matrix of weighted homogeneous polynomials and derivation algebras
• Computational aspects of the higher Nash blowup
• Non-normalized Nash blowup fails to resolve singularities in dimension three
• Derivations of negative degree on quasihomogeneous isolated complete\n intersection singularities
• Mather-Yau's type theorem for higher Nash blowup algebras