Completely lexsegment ideals

De Negri, Emanuela; Herzog, Jürgen

doi:10.1090/S0002-9939-98-04379-2

Completely lexsegment ideals
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by Emanuela De Negri and Jürgen Herzog PDF

Proc. Amer. Math. Soc. 126 (1998), 3467-3473 Request permission

Abstract:

In this paper we study ideals which are generated by lexsegments of monomials. In contrast to initial lexsegments, the shadow of an arbitrary lexsegment is in general not again a lexsegment. An ideal generated by a lexsegment is called completely lexsegment, if all iterated shadows of the set of generators are lexsegments. We characterize all completely lexsegment ideals and describe cases in which they have a linear resolution. We also prove a persistence theorem which states that all iterated shadows of a lexsegment are again lexsegments if the first shadow has this property.

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