Gotzmann monomials in four variables

Authors

  • Vittoria Bonanzinga Univ. Mediterranea di Reggio Calabria, DIIES, Via Graziella (Feo di Vito), 89100 Reggio Calabria, Italia
  • Shalom Eliahou UR 2597 – LMPA – Laboratoire de Mathématiques Pures et Appliquées Joseph Liouville, Univ. Littoral Côte d'Opale, F-62100 Calais, France and CNRS, FR2037, France

DOI:

https://doi.org/10.33044/revuma.v62n1a04

Abstract

It is a widely open problem to determine which monomials in the $n$-variable polynomial ring $K[x_1,\dots,x_n]$ over a field $K$ have the Gotzmann property, i.e. induce a Borel-stable Gotzmann monomial ideal. Since 2007, only the case $n \le 3$ was known. Here we solve the problem for the case $n=4$. The solution involves a surprisingly intricate characterization.

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Published

2021-05-21

Issue

Vol. 62 No. 1 (2021)

Section

Article

License

Copyright (c) 2021 Vittoria Bonanzinga, Shalom Eliahou

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