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arXiv · 2211.11026

Linear resolutions of $t$-spread lexsegment ideals via Betti splittings

Marilena Crupi·Antonino Ficarra
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Abstract

Let $S=K[x_1,\dots,x_n]$ 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.

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Marilena Crupi, Antonino Ficarra. 2022-11-20. Linear resolutions of $t$-spread lexsegment ideals via Betti splittings. https://arxiv.org/abs/2211.11026

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