Resolutions of monomial ideals and the Eliahou–Kervaire formula

  • Jürgen HerzogEmail author
  • Takayuki Hibi


Chapter 7 discusses minimal free resolutions of monomial ideals. We derive formulas for the graded Betti numbers of stable and squarefree stable ideals, and use these formulas to deduce the Bigatti–Hulett theorem which says that lexsegment ideals have the largest graded Betti numbers among all graded ideals with the same Hilbert function. We also present the squarefree analogue of the Bigatti–Hulett theorem, and give the comparison of Betti numbers over the symmetric and exterior algebra.


Short Exact Sequence Betti Number Homology Class Hilbert Function Monomial Ideal 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

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

Personalised recommendations