English

On minimal Gorenstein Hilbert function

Algebraic Geometry 2024-05-13 v3

Abstract

We conjecture that a class of Artinian Gorenstein Hilbert algebras called full Perazzo algebras always have minimal Hilbert function, fixing codimension and length. We prove the conjecture in length four and five, in low codimension. We also prove the conjecture for a particular subclass of algebras that occurs in every length and certain codimensions. As a consequence of our methods we give a new proof of part of a known result about the asymptotic behavior of the minimum entry of a Gorenstein Hilbert function.

Keywords

Cite

@article{arxiv.2206.05572,
  title  = {On minimal Gorenstein Hilbert function},
  author = {Lenin Bezerra and Rodrigo Gondim and Giovanna Ilardi and Giuseppe Zappalà},
  journal= {arXiv preprint arXiv:2206.05572},
  year   = {2024}
}

Comments

Accepted for publication in Revista de la Real Academia de Ciencias Exactas, F\'isicas y Naturales. Serie A. Matem\'aticas

R2 v1 2026-06-24T11:47:37.654Z