arXiv math/04115632004-11-24math.AC

Extending the idea of compressed algebra to arbitrary socle-vectors, II: cases of non-existence

Fabrizio Zanello

备注：: 34 pages (19 in the journal). With permission from Elsevier
发表信息：: J. of Algebra 275 (2004), No. 2, 730-748

英文摘要：

This paper is the continuation of the previous work on generalized compressed algebras (GCA's). First we exhibit a new class of socle-vectors $s$ which admit a GCA (whose $h$-vector is lower than the upper-bound $H$ of Theorem A of the previous paper). In particular, it follows that for every socle-vector $s$ of type 2 there exists a GCA (in any codimension $r$). The main result of this paper is the following: there exist pairs $(r,s)$ which do not admit a GCA. Moreover, the way this pathology occurs may be "arbitrarily bad" (even in codimension 3). Finally, we start considering the difficult problem of characterizing the pairs $(r,s)$ which admit a GCA, focusing on a particular class of socle-vectors of codimension 3.

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