Powers of monomial ideals

  • Jürgen HerzogEmail author
  • Takayuki Hibi


Chapter 10 is devoted to the study of powers of monomial ideals. We begin with a brief introduction to toric ideals and Rees algebras, and present a Gröbner basis criterion which guarantees that all powers of an ideal have a linear resolution. As an application it is shown that all powers of monomial ideals with 2-linear resolution have a linear resolution. Then the depth of powers of monomial ideals, and Mengerian and unimodular simplicial complexes are considered.


Bipartite Graph Vertex Cover Linear Resolution Chordal Graph Monomial Ideal 
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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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