Generic initial ideals

Jürgen Herzog () and Takayuki Hibi ()
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Jürgen Herzog: Universität Duisburg-Essen, Fachbereich Mathematik
Takayuki Hibi: Osaka University, Department of Pure and Applied Mathematics, Graduate School of Information Science and Technology

Chapter 4 in Monomial Ideals, 2011, pp 51-74 from Springer

Abstract: Abstract Chapter 4 concerns generic initial ideals. This theory plays an essential role in the combinatorial applications considered in Part III. Therefore, for the sake of completeness, we present in Chapter 4 the main theorems on generic initial ideals together with their complete proofs. Generic initial ideals are Borel-fixed. They belong to the more general class of Borel type ideals for which various characterizations are given. Generic annihilator numbers and extremal Betti numbers are introduced, and it is shown that extremal Betti numbers are invariant under taking generic initial ideals.

Keywords: Betti Number; Regular Sequence; Hilbert Function; Monomial Ideal; Zariski Open Subset (search for similar items in EconPapers)
Date: 2011
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DOI: 10.1007/978-0-85729-106-6_4

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