Monomial curve families supporting Rossi's conjecture

Arslan F., Sipahi N., Sahin N.

JOURNAL OF SYMBOLIC COMPUTATION, cilt.55, ss.10-18, 2013 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 55
  • Basım Tarihi: 2013
  • Doi Numarası: 10.1016/j.jsc.2013.03.002
  • Dergi Adı: JOURNAL OF SYMBOLIC COMPUTATION
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.10-18
  • Anahtar Kelimeler: Monomial curve, Symmetric numerical semigroup, Gluing, Gorenstein, Hilbert function of a local ring, Rossi's conjecture, HILBERT-FUNCTIONS, SEMIGROUPS
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

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.