Monomial ideals with tiny squares

Shalom Eliahou (1) , Jürgen Herzog (2) , Maryam Mohammadi Saem (3)

1 LMPA - Laboratoire de Mathématiques Pures et Appliquées Joseph Liouville
2 Universität Duisburg-Essen = University of Duisburg-Essen [Essen]
3 University of Mohaghegh Ardabili

Let I ⊂ K[x, y] be a monomial ideal. How small can µ(I^2) be in terms of µ(I)? It has been expected that the inequality µ(I^2) > µ(I) should hold whenever µ(I) ≥ 2. Here we disprove this expectation and provide a somewhat surprising answer to the above question.

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

Shalom Eliahou, Jürgen Herzog, Maryam Mohammadi Saem. Monomial ideals with tiny squares. 2018. ⟨hal-01691312⟩