Gotzmann Ideals and Applications to Graphs II

Abstract

Let k be an infinite field and S = k[x₁, . . . , x_n] the polynomial ring over k with each degx_i = 1 and m = (x₁ , . . . , x_n) 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.


[DOI: 10.1685/CSC06024] About DOI