A hyperplane restriction theorem and applications to reductions of ideals

Caviglia, Giulio

doi:10.1090/bproc/103

A hyperplane restriction theorem and applications to reductions of ideals
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by Giulio Caviglia HTML | PDF

Proc. Amer. Math. Soc. Ser. B 9 (2022), 325-335

Abstract:

Green’s general hyperplane restriction theorem gives a sharp upper bound for the Hilbert function of a standard graded algebra over an infinite field $K$ modulo a general linear form. We strengthen Green’s result by showing that the linear forms that do not satisfy such estimate belong to a finite union of proper linear spaces. As an application we give a method to derive variations of the Eakin-Sathaye theorem on reductions. In particular, we recover and extend results by O’Carroll on the Eakin-Sathaye theorem for complete and joint reductions.

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