Article ID Journal Published Year Pages File Type
5771720 Journal of Algebra 2017 21 Pages PDF
Abstract
In this paper we solve a problem posed by M.E. Rossi: Is the Hilbert function of a Gorenstein local ring of dimension one not decreasing? More precisely, for any integer h>1, h∉{14+22k,35+46k|k∈N}, we construct infinitely many one-dimensional Gorenstein local rings, included integral domains, reduced and non-reduced rings, whose Hilbert function decreases at level h; moreover, we prove that there are no bounds to the decrease of the Hilbert function. The key tools are numerical semigroup theory, especially some necessary conditions to obtain decreasing Hilbert functions found by the first and the third author, and a construction developed by V. Barucci, M. D'Anna and the second author, that gives a family of quotients of the Rees algebra. Many examples are included.
Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory
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