Monomial curve families supporting Rossi's conjecture

Arslan F., Sipahi N., Sahin N.

JOURNAL OF SYMBOLIC COMPUTATION, vol.55, pp.10-18, 2013 (SCI-Expanded, Scopus)

  • Publication Type: Article / Article
  • Volume: 55
  • Publication Date: 2013
  • Doi Number: 10.1016/j.jsc.2013.03.002
  • Journal Name: JOURNAL OF SYMBOLIC COMPUTATION
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.10-18
  • Keywords: Monomial curve, Symmetric numerical semigroup, Gluing, Gorenstein, Hilbert function of a local ring, Rossi's conjecture, HILBERT-FUNCTIONS, SEMIGROUPS
  • Middle East Technical University Affiliated: Yes

Abstract

In this article, we give a constructive method to form infinitely many families of monomial curves in affine 4-space with corresponding Gorenstein local rings in embedding dimension 4 supporting Rossi's conjecture. Starting with any monomial curve in affine 2-space, we obtain large families of Gorenstein local rings with embedding dimension 4, having non-decreasing Hilbert functions, although their associated graded rings are not Cohen-Macaulay. (C) 2013 Elsevier B.V. All rights reserved.