Let S = K[x_1,...,x_n] be a polynomial ring in n variables with coefficients over a field K. A t-spread lexsegment ideal I of S is a monomial ideal generated by a t-spread lexsegment set. We determine all t-spread lexsegment ideals with linear resolution by means of Betti splittings. As applications we provide formulas for the Betti numbers of such a class of ideals and furthermore we characterize all incompletely t-spread lexsegment ideals with linear quotients.
Linear resolutions of t -spread lexsegment ideals via Betti splittings
Crupi M.Primo
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2023-01-01
Abstract
Let S = K[x_1,...,x_n] be a polynomial ring in n variables with coefficients over a field K. A t-spread lexsegment ideal I of S is a monomial ideal generated by a t-spread lexsegment set. We determine all t-spread lexsegment ideals with linear resolution by means of Betti splittings. As applications we provide formulas for the Betti numbers of such a class of ideals and furthermore we characterize all incompletely t-spread lexsegment ideals with linear quotients.File in questo prodotto:
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