Monomial ideals of minimal depth and trivial modifications

Details Monomial ideals of minimal depth and trivial modifications Monomial ideals of minimal depth and trivial modifications

2012-03-15

arxiv.org/abs/1203.3319v1

Mathematics

Commutative Algebra

7 pages

Scientific paper

Let $S$ be a polynomial algebra over a field. We study classes of monomial
ideals (as for example lexsegment ideals) of $S$ having minimal depth. In
particular, Stanley's conjecture holds for these ideals. Also we show that if
Stanley's conjecture holds for a square free monomial ideal then it holds for
all its trivial modifications.

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