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

By Nguyên Công Minh, Ngô Viêt Trung. 2010

78 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Pharmacology

View Paper: https://www.semanticscholar.org/paper/588f5002410c3ddbb7a33721b3181ba6547418a0

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Citations in the corpus

Matroid configurations and symbolic powers of their ideals (2015, background): “It was shown independently in [33] and [25] that, for each positive integer m, the ideal”
Star configurations in Pn (2013, background): “We now recall a key fact from [23] and [27]:”