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Gluing and Hilbert functions of monomial curves
Hilbert function of local ring tangent cone monomial curve numerical semigroup semigroup gluing
2011/8/26
Abstract: In this article, by using the technique of gluing semigroups, we give infinitely many families of 1-dimensional local rings with non-decreasing Hilbert functions. More significantly, these a...
On Unimodality of Hilbert Functions of Gorenstein Artin Algebras of Embedding Dimension Four
Hilbert Functions Gorenstein Artin Algebras
2010/11/18
We prove that the Hilbert functions of codimension four graded Gorenstein Artin algebras R/I are unimodal provided I has a minimal generator in degree less than five. It is an open question whether al...
For a standard graded algebra R, we consider embeddings of the the poset of Hilbert functions
of quotients of R into the poset of ideals of R, as a way of classification of Hilbert functions. There a...