Existence of a Nonsmoothable Local Gorenstein Algebra with Smoothable Q(0)

Ruoyu Wu

Existence of a Nonsmoothable Local Gorenstein Algebra with Smoothable Q(0)

Commutative Algebra 2026-07-02 v1 Algebraic Geometry

Authors: Ruoyu Wu

Abstract

We prove that there exists a local Artinian Gorenstein algebra $A$ which is not smoothable, although the first symmetric quotient $Q_A(0)$ in the symmetric decomposition of the associated graded algebra is smoothable. The proof uses divided-power inverse systems and gives such algebras of length $31$ and embedding dimension $14$ over every algebraically closed field.

Keywords

Gorenstein algebras smoothability divided-power inverse systems local Artinian algebras symmetric decomposition

Cite

@article{arxiv.2607.01683,
  title  = {Existence of a Nonsmoothable Local Gorenstein Algebra with Smoothable Q(0)},
  author = {Ruoyu Wu},
  journal= {arXiv preprint arXiv:2607.01683},
  year   = {2026}
}