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; L., Sorrenti. - 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.
2007
Gotzmann ideal; Gotzmann graph; principal Borel ideals
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.12318/5691
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