  This paper is a contribution to the study of the geometry of algebras related
the Weyl groupoid initiated in \cite{M22}. The Nullstellensatz gives a
bijection between radical ideals of such an algebra and their zero loci, the
superalgebraic sets. Such sets are exactly the (Zariski) closed sets that are
invariant under the action of a suitable groupoid, and the smallest
superalgebraic set containing a given closed set can be described explicitly.
Here we give several examples of superalgebraic sets. We also give several
characterizations of Laurent supersymmetric polynomials. These adapt to unite
several definitions of one of the algebras of interest, $J(G)$ that may be
found in the literature.
