Abstract
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.
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© 2011 Springer-Verlag London Limited
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Herzog, J., Hibi, T. (2011). Resolutions of monomial ideals and the Eliahou–Kervaire formula. In: Monomial Ideals., vol 260. Springer, London. https://doi.org/10.1007/978-0-85729-106-6_7
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DOI: https://doi.org/10.1007/978-0-85729-106-6_7
Publisher Name: Springer, London
Print ISBN: 978-0-85729-105-9
Online ISBN: 978-0-85729-106-6
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