On the growth of deviations

Boocher, Adam; D’Alì, Alessio; Grifo, Eloísa; Montaño, Jonathan; Sammartano, Alessio

doi:10.1090/proc/13132

On the growth of deviations
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by Adam Boocher, Alessio D’Alì, Eloísa Grifo, Jonathan Montaño and Alessio Sammartano PDF

Proc. Amer. Math. Soc. 144 (2016), 5049-5060 Request permission

Abstract:

The deviations of a graded algebra are a sequence of integers that determine the Poincaré 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 increase 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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