GLUING AND HILBERT FUNCTIONS OF MONOMIAL CURVES

Arslan F., METE P., Sahin M.

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, cilt.137, sa.7, ss.2225-2232, 2009 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 137 Sayı: 7
  • Basım Tarihi: 2009
  • Dergi Adı: PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.2225-2232
  • Anahtar Kelimeler: Hilbert function of local ring, tangent cone, monomial curve, numerical semigroup, semigroup gluing, nice gluing, Rossi's conjecture, COMPLETE INTERSECTION, COHEN-MACAULAYNESS
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

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.