Let k be an infinite field and S = k[x1, . . . , xn] the polynomial ring over k with each degxi = 1 and m = (x1 , . . . , xn ) the graded maximal ideal of S. A graded ideal I generated in degree d is called a Gotzmann ideal if the number of generators of mI is the smallest possible, namely, equal to the number of generators of (mI)lex. A graph G is called Gotzmann if the edge ideal I(G) is a Gotzmann ideal. We determine some classes of Gotzmann graphs and we characterize all Cohen-Macaulay graphs which are Gotzmann and principal Borel.

Gotzmann Ideals and applications to graphs

BONANZINGA, Vittoria;
2007

Abstract

Let k be an infinite field and S = k[x1, . . . , xn] the polynomial ring over k with each degxi = 1 and m = (x1 , . . . , xn ) the graded maximal ideal of S. A graded ideal I generated in degree d is called a Gotzmann ideal if the number of generators of mI is the smallest possible, namely, equal to the number of generators of (mI)lex. A graph G is called Gotzmann if the edge ideal I(G) is a Gotzmann ideal. We determine some classes of Gotzmann graphs and we characterize all Cohen-Macaulay graphs which are Gotzmann and principal Borel.
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/20.500.12318/5691
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus ND
  • ???jsp.display-item.citation.isi??? ND
social impact