Alexander duality and resolutions

  • Jürgen Herzog
  • Takayuki Hibi


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.


Simplicial Complex Linear Resolution Monomial Ideal Minimal Prime Ideal Grade Betti Number 
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Copyright information

© Springer-Verlag London Limited 2011

Authors and Affiliations

  1. 1.Fachbereich MathematikUniversität Duisburg-EssenEssenGermany
  2. 2.Department of Pure and Applied Mathematics, Graduate School of Information Science and TechnologyOsaka UniversityToyonakaJapan

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