GLUING AND HILBERT FUNCTIONS OF MONOMIAL CURVES


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Arslan F., Mete P., Sahin M.

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, cilt.137, sa.7, ss.2225-2232, 2009 (SCI-Expanded) identifier identifier

Özet

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 are local rings whose associated graded rings are not necessarily Cohen-Macaulay. In this sense, we give an effective technique for constructing large families of 1-dimensional Gorenstein local rings associated to monomial curves, which support Rossi's conjecture saying that every Gorenstein local ring has a non-decreasing Hilbert function.