Artinian level algebras of low socle degree

2012/08/16 by Alessandro De Stefani, De Stefani, Alessandro
Mathematics · #13H10 #13H15 #14C05 #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #msc:13H10 #msc:13H15 #msc:14C05

paper · pdf · doi:10.48550/arxiv.1208.3506

24 pages. To appear on "Communications in Algebra"

arxiv created 2012/08/16 · arxiv updated 2012/08/20

Abstract

In this paper we study Hilbert functions and isomorphism classes of Artinian level local algebras via Macaulay's inverse system. Upper and lower bounds concerning numerical functions admissible for level algebras of fixed type and socle degree are known. For each value in this range we exhibit a level local algebra with that Hilbert function, provided that the socle degree is at most three. Furthermore we prove that level local algebras of socle degree three and maximal Hilbert function are graded. In the graded case the extremal strata have been parametrized by Cho and Iarrobino.

Related

• Hilbert functions of graded algebras over Artinian rings
• Hilbert functions of Gorenstein algebras associated to a pencil of forms
• Artinian level algebras of codimension 3
• Generic Initial Ideals And Graded Artinian Level Algebras Not Having The Weak-Lefschetz Property
• Non-Level O-sequences of Codimension 3 and Degree of The Socle Elements