Publications [#243917] of Ezra Miller

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Peer-reviewed journal articles published

1. with Miller, E; Sturmfels, B; Yanagawa, K. "Generic and cogeneric monomial ideals." Journal of Symbolic Computation 29.4-5 (January, 2000): 691-708. (Symbolic computation in algebra, analysis, and geometry (Berkeley, CA, 1998)) [MR2001m:13051], [doi]
   (last updated on 2024/04/19)

   Abstract:
   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.