Chapter 8 begins with Hochster’s formula to compute the graded Betti numbers of Stanley–Reisner ideals and Reisner’s Cohen–Macaulay criterion for simplicial complexes. Then the Eagon–Reiner theorem and variations of it are discussed. In particular, ideals with linear quotients, componentwise linear ideals, sequentially Cohen–Macaulay ideals and shellable simplicial complexes are studied.
KeywordsSimplicial Complex Linear Resolution Monomial Ideal Minimal Prime Ideal Grade Betti Number
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