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, V., L., S.. - In: COMMUNICATIONS TO SIMAI CONGRESS. - ISSN 1827-9015. - 2:(2007), pp. 1-7. [10.1685/CSC06024]
Gotzmann Ideals and applications to graphs
BONANZINGA, Vittoria;
2007-01-01
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
