Let $X=P^{k_1}\times \ldots \times P^{k_r}$ be the product of several complex projective spaces ($P^k$ is the projectivization of $\mathbb{C}^{k+1}$) in the Segre embedding into $P=P^{(k_1+1)\cdots(k_r+1)-1}$. The $X$-discriminant is the equation of the projective dual variety of $X$ in $P^*$. In the book of Gelfand, Kapranov and Zelevinsky the hyperdeterminant Det (of format $(k_1+1)\times \ldots \times (k_r+1)$) is defined to be the $X$-discriminant, which is a homogeneous polynomial. Now they say that this is determined uniquely (up to sign) by the requirement that Det has integral coefficients and is irreducible over $\mathbb{Z}$.

Why is this so? Or more precisely, why can we require that it has integral coeffients?