English

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}
}