If a group $G$ acts on an affine variety $X$, and $W$ is a $G$-module, a covariant on $X$ with values in $W$ is a regular function $X\to V$ W$which is$G$-equivariant. In the special case in which$G=\mathrm{SL}(V)$is the special linear group on a vector space$V$,$X=\mathrm{Pol}_{d_1}(V)\otimes\cdots\otimes\mathrm{Pol}_{d_s}(V)$and$W=\mathrm{Pol}_{d}(V)$, with natural actions of$G$, a covariant$X\to W$is called a concomitant of degree$d$. The canonical example of a concomitant is the resultant$R(f_1,\dots,f_s)$of$s$homogeneous polynomial functions$f_1\in\mathrm{Pol}_{d_1}(V), \dots, f_s\in\mathrm{Pol}_{d_s}(V)$of degrees$d_1,\dots,d_s$, which has degree$0$. A simpler example is the Jacobian of$n$homogeneous forms in$n$variables. 1 If a group$G$acts on an affine variety$X$, and$W$is a$G$-module, a covariant on$X$with values in$W$is a regular function$X\to V$which is$G$-equivariant. In the special case in which$G=\mathrm{SL}(V)$is the special linear group on a vector space$V$,$X=\mathrm{Pol}_{d_1}(V)\otimes\cdots\otimes\mathrm{Pol}_{d_s}(V)$and$W=\mathrm{Pol}_{d}(V)$, with natural actions of$G$, a covariant$X\to W$is called a concomitant of degree$d$. The canonical example of a concomitant is the resultant$R(f_1,\dots,f_s)$of$s$homogeneous polynomial functions$f_1\in\mathrm{Pol}_{d_1}(V), \dots, f_s\in\mathrm{Pol}_{d_s}(V)$of degrees$d_1,\dots,d_s$, which has degree$0$. A simpler example is the Jacobian of$n$homogeneous forms in$n\$ variables.