ARTINIAN LEVEL ALGEBRAS OF LOW SOCLE DEGREE

作者：De Stefani Alessandro^*

来源：Communications in Algebra, 2014, 42(2): 729-754.

DOI：10.1080/00927872.2012.722736

• Artinian level local algebras
• Hilbert functions
• Inverse system
• Isomorphism classes

In this article 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.

• 出版日期2014-2-1