Superspace: a Comfortably Vast Algebraic Variety

Supersymmetry has been studied for over three decades by physicists, its superset even longer by mathematicians, and superspace has proven to be very useful both conceptually and in facilitating computations. However, the (1) necessary existence of superspace has been doubted, and its (2) properties and (3) applications have not been understood in general. Herein, all doubt is removed from the first of these: superspace must exist. Further study then reveals a perhaps surprising size and algebro-geometric structure of this extension of spacetime.