Extending the idea of compressed algebra to arbitrary socle-vectors
| dc.creator | Zanello, Fabrizio | |
| dc.date | 2004-11-24 | |
| dc.date.accessioned | 2026-07-07T05:14:41Z | |
| dc.date.available | 2026-07-07T05:14:41Z | |
| dc.description | Fix a codimension $r$ and a socle-vector $s$. Is there an (entry by entry) maximal $h$-vector $h$ among the $h$-vectors of all the (standard graded artinian) algebras having data $(r,s)$? Extending a definition of Iarrobino, if such an $h$ exists, we define as {\it generalized compressed} (GCA, in brief) any algebra having the data $(r,s,h)$. The two main results of this paper are: Theorem A, where we supply a very natural upper-bound $H$ for all the $h$-vectors possible for a given pair $(r,s)$; Theorem B, which asserts that, under certain conditions on the pair $(r,s)$, the upper-bound $H$ of Theorem A is actually achieved by a GCA. In particular, it follows that, when $r=2$, there always exists a GCA (having $h$-vector $H$). Moreover, we show that, in general, the hypotheses of Theorem B cannot be improved, i.e., under weaker conditions on the pair $(r,s)$, the upper-bound $H$ above is not always achieved. | |
| dc.description | 31 pages (18 in the journal). With permission from Elsevier | |
| dc.identifier | https://arxiv.org/abs/math/0411562 | |
| dc.identifier | http://arxiv.org/abs/math/0411562 | |
| dc.identifier | J. of Algebra 270 (2003), No. 1, 181-198 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/73369 | |
| dc.subject | Commutative Algebra | |
| dc.subject | 13E10 | |
| dc.title | Extending the idea of compressed algebra to arbitrary socle-vectors | |
| dc.type | text |