Generic and Cogeneric Monomial Ideals

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dc.creatorMiller, Ezra
dc.creatorSturmfels, Bernd
dc.creatorYanagawa, Kohji
dc.date1998-12-22
dc.date.accessioned2026-07-07T05:27:20Z
dc.date.available2026-07-07T05:27:20Z
dc.descriptionMonomial 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.
dc.description15 pages, LaTeX
dc.identifierhttps://arxiv.org/abs/math/9812126
dc.identifierhttp://arxiv.org/abs/math/9812126
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/77880
dc.subjectCommutative Algebra
dc.subjectAlgebraic Geometry
dc.subjectCombinatorics
dc.subject13D02, 13H10, 13P10 (Primary); 52B20, 05E99 (Secondary)
dc.titleGeneric and Cogeneric Monomial Ideals
dc.typetext

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