Level algebras with bad properties
| dc.creator | Boij, Mats | |
| dc.creator | Zanello, Fabrizio | |
| dc.date | 2005-12-09 | |
| dc.date | 2006-05-18 | |
| dc.date.accessioned | 2026-07-07T09:31:22Z | |
| dc.date.available | 2026-07-07T09:31:22Z | |
| dc.description | This paper can be seen as a continuation of the works contained in the recent preprints [Za], of the second author, and [Mi], of Juan Migliore. Our results are: 1). There exist codimension three artinian level algebras of type two which do not enjoy the Weak Lefschetz Property (WLP). In fact, for $e\gg 0$, we will construct a codimension three, type two $h$-vector of socle degree $e$ such that {\em all} the level algebras with that $h$-vector do not have the WLP. We will also describe the family of those algebras and compute its dimension, for each $e\gg 0$. 2). There exist reduced level sets of points in ${\mathbf P}^3$ of type two whose artinian reductions all fail to have the WLP. Indeed, the examples constructed here have the same $h$-vectors we mentioned in 1). 3). For any integer $r\geq 3$, there exist non-unimodal monomial artinian level algebras of codimension $r$. As an immediate consequence of this result, we obtain another proof of the fact (first shown by Migliore in [Mi], Theorem 4.3) that, for any $r\geq 3$, there exist reduced level sets of points in ${\mathbf P}^r$ whose artinian reductions are non-unimodal. | |
| dc.description | 10 pages; a few minor changes; to appear in the Proc. of the AMS | |
| dc.identifier | https://arxiv.org/abs/math/0512198 | |
| dc.identifier | http://arxiv.org/abs/math/0512198 | |
| dc.identifier | Proc. Amer. Math. Soc. 135 (2007), no. 9, 2713-2722 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/158435 | |
| dc.subject | Commutative Algebra | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Primary: 13H10; Secondary: 13D40, 13E10, 14M05 | |
| dc.title | Level algebras with bad properties | |
| dc.type | text |