Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

Completely lexsegment ideals

Author(s): Emanuela De Negri; Jürgen Herzog
Journal: Proc. Amer. Math. Soc. 126 (1998), 3467-3473.
MSC (1991): Primary 13C99, 13D02
MathSciNet review: 1452799
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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.

References:

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