The $h$-vector of a relatively compressed level algebra

Details The $h$-vector of a relatively compressed level algebra The $h$-vector of a relatively compressed level algebra

2005-03-24

arxiv.org/abs/math/0503526v2

Comm. in Algebra 35 (2007), No. 4, 1087-1091

Mathematics

Commutative Algebra

7 pages. A few minor changes. To appear in Comm. in Algebra

Scientific paper

The purpose of this note is to supply an upper and a lower bound (which are in general sharp) for the $h$-vector of a level algebra which is relatively compressed with respect to any arbitrary level algebra $A$. The useful concept of relatively compressed algebra was recently introduced in $[MMN]$ by Migliore {\it et al.} (whose investigations mainly focused on the particular case of $A$ a complete intersection). The key idea of this note is the simple observation that the level algebras which are relatively compressed with respect to $A$ coincide (after an obvious isomorphism) with the generic level quotients of suitable truncations of $A$. Therefore, we are able to apply to relatively compressed algebras the main result of our recent work $[Za3]$.

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