Level Algebras of Type 2

ABSTRACT

In this article, we study standard graded Artinian level algebras, in particular those whose socle-vector has type 2. Our main results are: the characterization of the level h-vectors of the form (1, r,…,r, 2) for r ≤ 4; the characterization of the minimal free resolutions associated to each of the h-vectors above when r = 3; a sharp upper-bound (under certain mild hypotheses) for the level h-vectors (1,r,…,a, 2) of arbitrary codimension r and type 2, which depends on the next to last entry a.

Key Words:

• Artinian graded algebras
• h-vectors
• Inverse systems
• Level algebras
• Minimal free resolutions
• Socle-vectors

Mathematics Subject Classification:

• Primary 13E10
• Secondary 13H10

ACKNOWLEDGMENTS

We wish to express our warm gratitude to Professor Anthony Iarrobino for sending us the first draft of Iarrobino (to appear) and for his interesting comments on a previous version of this work, and to Professor Mike Roth for giving us a copy of his result (Lemma 4.3).

The results obtained in this article are part of the author's Ph.D. dissertation, written at Queen's University (Kingston, Ontario, Canada), under the supervision of Professor A. V. Geramita.

Notes

Communicated by W. Bruns.