Cohen-Macaulayness of monomial ideals and symbolic powers of Stanley-Reisner ideals

Details Cohen-Macaulayness of monomial ideals and symbolic powers of Stanley-Reisner ideals Cohen-Macaulayness of monomial ideals and symbolic powers of Stanley-Reisner ideals

2010-03-10

arxiv.org/abs/1003.2152v2

Adv. Math. 226 (2011), 1285-1306

Mathematics

Commutative Algebra

The published version of this paper contains a gap in the proofs of Theorem 2.5 and Theorem 3.5. This version corrects the pro

Scientific paper

We present criteria for the Cohen-Macaulayness of a monomial ideal in terms of its primary decomposition. These criteria allow us to use tools of graph theory and of linear programming to study the Cohen-Macaulayness of monomial ideals which are intersections of prime ideal powers. We can characterize the Cohen-Macaulayness of the second symbolic power or of all symbolic powers of a Stanley-Reisner ideal in terms of the simplicial complex. These characterizations show that the simplicial complex must be very compact if some symbolic power is Cohen-Macaulay. In particular, all symbolic powers are Cohen-Macaulay if and only if the simplicial complex is a matroid complex. We also prove that the Cohen-Macaulayness can pass from a symbolic power to another symbolic powers in different ways.

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