Generic and cogeneric monomial ideals

Journal Article (Journal Article)

Monomial ideals which are generic with respect to either their generators or irreducible components have minimal free resolutions encoded by simplicial complexes. There are numerous equivalent ways to say that a monomial ideal is generic or cogeneric. 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. © 2000 Academic Press.

Full Text

Duke Authors

Cited Authors

  • Miller, E; Sturmfels, B; Yanagawa, K

Published Date

  • January 1, 2000

Published In

Volume / Issue

  • 29 / 4-5

Start / End Page

  • 691 - 708

International Standard Serial Number (ISSN)

  • 0747-7171

Digital Object Identifier (DOI)

  • 10.1006/jsco.1999.0290

Citation Source

  • Scopus