GLUING AND HILBERT FUNCTIONS OF MONOMIAL CURVES


Arslan F., METE P., Sahin M.

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, vol.137, no.7, pp.2225-2232, 2009 (Journal Indexed in SCI) identifier

  • Publication Type: Article / Article
  • Volume: 137 Issue: 7
  • Publication Date: 2009
  • Title of Journal : PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
  • Page Numbers: pp.2225-2232
  • Keywords: Hilbert function of local ring, tangent cone, monomial curve, numerical semigroup, semigroup gluing, nice gluing, Rossi's conjecture, COMPLETE INTERSECTION, COHEN-MACAULAYNESS

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 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.