Related papers: Empty simplices of polytopes and graded Betti numb…

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A foundational principle in the study of modules over standard graded polynomial rings is that geometric positivity conditions imply vanishing of Betti numbers. The main goal of this paper is to determine the extent to which this principle…

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We are interested in algebraic properties of empty lattice simplices $\Delta$, that is, $d$-dimensional lattice polytopes containing exactly $d+1$ points of the integer lattice $\mathbb{Z}^d$. The cyclicity rank of $\Delta$ is the minimal…