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arXiv · 1504.01066

On the growth of deviations

Adam Boocher·Alessio D'Alì·Eloísa Grifo·Jonathan Montaño·Alessio Sammartano
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Abstract

The deviations of a graded algebra are a sequence of integers that determine the Poincare series of its residue field and arise as the number of generators of certain DG algebras. In a sense, deviations measure how far a ring is from being a complete intersection. In this paper we study extremal deviations among those of algebras with a fixed Hilbert series. In this setting, we prove that, like the Betti numbers, deviations do not decrease when passing to an initial ideal and are maximized by the Lex-segment ideal. We also prove that deviations grow exponentially for Golod rings and for certain quadratic monomial algebras.

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Adam Boocher, Alessio D'Alì, Eloísa Grifo, Jonathan Montaño, Alessio Sammartano. 2015-04-04. On the growth of deviations. https://doi.org/10.1090/proc/13132

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