Gotzmann monomials in four variables

Vittoria Bonanzinga , Shalom Eliahou (1)

1 LMPA - Laboratoire de Mathématiques Pures et Appliquées Joseph Liouville

It is a widely open problem to determine which monomials in the n-variable polynomial ring K[x_1,...,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 ≤ 3 was known. Here we solve the problem for the case n = 4. The solution involves a surprisingly intricate characterization.

Mots clés: Gotzmann persistence theorem; Gotzmann ideal; Lexsegment; Borel-stable ideal; Monomial ideal

Domaines: Algèbre commutative [math.AC]; Combinatoire [math.CO]

Vittoria Bonanzinga, Shalom Eliahou. Gotzmann monomials in four variables. Revista de la Unión Matemática Argentina, 2021, 62 (1), pp.67-93. ⟨10.33044/revuma.v62n1a04⟩. ⟨hal-02179711v2⟩