Generic and Cogeneric Monomial Ideals

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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.
15 pages, LaTeX

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Commutative Algebra, Algebraic Geometry, Combinatorics, 13D02, 13H10, 13P10 (Primary); 52B20, 05E99 (Secondary)

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http://salesiana.dossiersoluciones.com/handle/123456789/77880

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/9812126
 http://arxiv.org/abs/math/9812126

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arXiv