Abstract:We introduce a construction, called linearization, that associates to any monomial ideal I ⊂ K[x 1 , . . . , x n ] an ideal Lin(I) in a larger polynomial ring. The main feature of this construction is that the new ideal Lin(I) has linear quotients. In particular, since Lin(I) is generated in a single degree, it follows that Lin(I) has a linear resolution. We investigate some properties of this construction, such as its interplay with classical operations on ideals, its Betti numbers, functoriality and combinat… Show more
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