Generic and Cogeneric Monomial Ideals
交换代数
2007-05-23 v1 代数几何
组合数学
摘要
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.
引用
@article{arxiv.math/9812126,
title = {Generic and Cogeneric Monomial Ideals},
author = {Ezra Miller and Bernd Sturmfels and Kohji Yanagawa},
journal= {arXiv preprint arXiv:math/9812126},
year = {2007}
}
备注
15 pages, LaTeX