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.
KeywordsBetti Number Regular Sequence Hilbert Function Monomial Ideal Zariski Open Subset
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