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Publications [#243917] of Ezra Miller
Papers Published
 with Miller, E; Sturmfels, B; Yanagawa, K, Generic and cogeneric monomial ideals,
Journal of Symbolic Computation, vol. 29 no. 45
(2000),
pp. 691708 (Symbolic computation in algebra, analysis, and geometry (Berkeley, CA, 1998).) [MR2001m:13051]
(last updated on 2017/12/18)
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 CohenMacaulay property implies shellability for both the Scarf complex and the StanleyReisner complex. Reverse lexicographic initial ideals of generic lattice ideals are generic. CohenMacaulayness for cogeneric ideals is characterized combinatorially; in the cogeneric case, the CohenMacaulay 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.


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