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Generic and Cogeneric Monomial Ideals

Ezra Miller·Bernd Sturmfels·Kohji Yanagawa
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Abstract

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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Ezra Miller, Bernd Sturmfels, Kohji Yanagawa. 1998-12-22. Generic and Cogeneric Monomial Ideals. https://arxiv.org/abs/math/9812126

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