On the Structure of Second Jacobian Ideals
arXiv:2411.15097 · doi:10.1007/s13366-025-00791-0
Abstract
We show that the second Jacobian ideal of a hypersurface can be decomposed such that a power of the Jacobian ideal becomes a factor. As an application of the decomposition, we present an elementary proof establishing that the second Nash blow-up algebra of a hypersurface singularity is a contact invariant.
Final version. Corrected typos and enhanced proofs based on the referee's suggestions. To appear in Beitr Algebra Geom