  Classically, B\'ezout's theorem says that an intersection of hypersurfaces in
a projective space is rationally equivalent to a number of copies of a smaller
projective space, the number depending on the degrees of the hypersurfaces. We
give a generalization of that result to the context of $C_2$-equivariant
hypersurfaces in $C_2$-equivariant linear projective space, expressing the
intersection as a linear combination of equivariant Schubert varieties.
