Reconstruction of a Hypersurface Singularity from its Moduli Algebra

Abstract

In this paper we present a constructive method to characterize ideals of the local ring ${\mathcal{O}}_{{\mathbb{C}}^n,0}$ of germs of holomorphic functions at $0\in {\mathbb{C}}^n$ which arise as the moduli ideal $⟨f,\mathfrak{m}j(f)⟩$, for some $f\in \mathfrak{m}\subset {\mathcal{O}}_{{\mathbb{C}}^n,0}$. A consequence of our characterization is an effective solution to a problem dating back to the 1980's, called the Reconstruction Problem of the hypersurface singularity from its moduli algebra. Our results work regardless of whether the hypersurface singularity is isolated or not.

11 pages now. Minor improvements in the Introduction. Better illustrative examples, I believe

References in corpus (2)

• Hypersurface singularities with monomial Jacobian ideal
• On Tjurina Ideals of Hypersurface Singularities