1998/12/22 by Ezra Miller, Bernd Sturmfels, Miller, Ezra +3
Mathematics · #05E99 (Secondary) #13D02 #13H10 #13P10 (Primary) #52B20 #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #math.AG #math.CO #msc:05E99 #msc:13D02 #msc:13H10 #msc:13P10 #msc:52B20
paper · pdf · doi:10.48550/arxiv.math/9812126
15 pages, LaTeX
arxiv created 1998/12/22 · arxiv updated 2009/11/30
Monomial 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.