Publications [#243917] of Ezra Miller

Papers Published

1. with Miller, E; Sturmfels, B; Yanagawa, K, Generic and cogeneric monomial ideals, Journal of Symbolic Computation, vol. 29 no. 4-5 (January, 2000), pp. 691-708, Elsevier BV (Symbolic computation in algebra, analysis, and geometry (Berkeley, CA, 1998).) [MR2001m:13051], [doi]
   (last updated on 2026/01/15)

   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.