by S.Yu. Orevkov

We prove that the (n-1)-dimensional volume of the Newton polytope of the discriminant of the monic polynomial of degree n in one variable with indeterminate coefficients is equal to $2^{n-1}n^{n-2}/n!$ (the volume is normalised so that the volume of a fundamental parallelepiped of the integral lattice is one). We prove also that the volume of the Newton polytope of the discriminant of a polynomial of degree d in m variables is greater than $C(d)m^d$ where C(d) is some constant which depend on d.