Gluing and Hilbert functions of monomial curves
Algebraic Geometry
2014-10-15 v1 Commutative Algebra
Combinatorics
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 are local rings whose associated graded rings are not necessarily Cohen-Macaulay. In this sense, we give an effective technique to construct large families of 1-dimensional Gorenstein local rings associated to monomial curves, which support Rossi's conjecture saying that every Gorenstein local ring has non-decreasing Hilbert function.
Keywords
Cite
@article{arxiv.1107.1328,
title = {Gluing and Hilbert functions of monomial curves},
author = {Feza Arslan and Pınar Mete and Mesut Şahin},
journal= {arXiv preprint arXiv:1107.1328},
year = {2014}
}