On the diameter of an ideal

We begin the study of the notion of diameter of an ideal I⊂S=k[x1,…,xn], an invariant measuring the distance between the minimal primes of I. We provide large classes of Hirsch ideals, i.e. ideals satisfying diam(I)≤height(I), such as: quadratic radical ideals such that S/I is Gorenstein and height(I)≤4, or ideals admitting a square-free complete intersection initial ideal.