TITLE: Term for the "nullspace" of a nonlinear system of equations
QUESTION [5 upvotes]: Just a quick terminology question. 
The set of solutions to a linear system of equations with nonunique solutions is known as the "nullspace".
What is the equivalent terminology (if there is one) for the nonunique solutions to a nonlinear system of equations? (or its equivalent Groebner basis)
For example:
$$
\begin{align}
&x_{1} + x_{2}^{2} + 3x_{3}= 0\\
&x_{3} = 2
\end{align}
$$
Is there a name this set of solutions? 
The solutions of the above system is:
$$
\begin{align}
&x_{1} = -6 -t^{2}\\
&x_{2} = t\\
&x_{3} = 2
\end{align}
$$

REPLY [3 votes]: Zero set is a usual term. But so is set of solutions. Zero set is applied to sets of functions. Set of solutions is applied to systems of equations.