Dehn functions of subgroups of products of free groups. Part II: Precise computations

We prove that the Bridson-Dison group has quartic Dehn function, thereby providing the first precise computation of the Dehn function of a subgroup of a direct product of free groups with super-quadratic Dehn function. We also prove that coabelian subgroups of direct products of $n$ free groups of finiteness type ${\mathcal{F}}_{n-1}$ and of corank $r\le n-2$ have quadratic Dehn functions.