Generic and Cogeneric Monomial Ideals

Details Generic and Cogeneric Monomial Ideals Generic and Cogeneric Monomial Ideals

1998-12-22

arxiv.org/abs/math/9812126v1

Mathematics

Commutative Algebra

15 pages, LaTeX

Scientific paper

Monomial ideals which are generic with respect to either their generators or irreducible components have minimal free resolutions derived from simplicial complexes. For a generic monomial ideal, the associated primes satisfy a saturated chain condition, and the Cohen-Macaulay property implies shellability for both the Scarf complex and the Stanley-Reisner complex. Reverse lexicographic initial ideals of generic lattice ideals are generic. Cohen-Macaulayness for cogeneric ideals is characterized combinatorially; in the cogeneric case the Cohen-Macaulay type is greater than or equal to the number of irreducible components. Methods of proof include Alexander duality and Stanley's theory of local h-vectors.

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