The realization space is
  [1                                 x1   1   0                       x1*x2                                           x1                                 x1    0   0    1    1]
  [1   x1*x2^2 + x1*x2 - x1 - x2^2 + x2   0   1   -x1*x2^2 + x1 + x2^2 - x2   -x1*x2^3 - x1*x2^2 + 2*x1*x2 + x2^3 - x2^2   x1*x2^2 + x1*x2 - x1 - x2^2 + x2   x1   0   x1    0]
  [1   x1*x2^2 + x1*x2 - x1 - x2^2 + x2   0   0                       x1*x2             x1*x2^2 + x1*x2 - x1 - x2^2 + x2                                  0   x2   1   x2   x3]
in the multivariate polynomial ring in 3 variables over ZZ
within the vanishing set of the ideal
Ideal (x1^2 + x1*x2^3 + x1*x2^2 - 2*x1*x2 - x2^3 + x2^2)
avoiding the zero loci of the polynomials
RingElem[x1*x3 - x1 + x2 - x3, x1^2*x2^2 + x1^2*x2 - x1^2*x3 - x1^2 - x1*x2^3 + x1*x2^2*x3 - 2*x1*x2^2 + x1*x2*x3 + 2*x1*x2 - x1*x3 + x2^3 - x2^2*x3 - x2^2 + x2*x3, x1, x3, x2 - x3, x1^2*x2*x3 - x1^2*x2 - x1*x2^3 + x1*x2^2*x3 + x1*x2 - x1*x3 + x2^3 - x2^2*x3 - x2^2 + x2*x3, x2 - 1, x1*x2 + x1 - x2, x1^2*x3 + x1*x2^3 - x1*x2^2*x3 + x1*x2^2 - x1*x2*x3 - x1*x2 + x1*x3 - x2^3 + x2^2*x3 + x2^2 - x2*x3, x1*x2^2 + x1*x2 - x1 - x2^2 + x2, x1*x3 - x1 + x2, x1^2*x2^2 + x1^2*x2 - x1^2*x3 - x1^2 - x1*x2^3 - 2*x1*x2^2 + 2*x1*x2 + x2^3 - x2^2, x2, x1^2*x3 - x1^2 - x1*x2^2 + x1 + x2^2 - x2, x1*x2^2 - x1*x3 - x1 - x2^2 + x2, x1^2*x3 + x1*x2^3 + x1*x2^2 - x1*x2 - x2^3 + x2^2, x1*x2^2*x3 - x1*x2^2 + x1*x2*x3 - x1*x2 - 2*x1*x3 + x1 - x2^2*x3 + x2^2 + x2*x3 - x2, x1*x2^3*x3 - x1*x2^3 + 2*x1*x2^2*x3 - x1*x2^2 - x1*x2*x3 + x1*x2 - x1*x3 - x2^3*x3 + x2^3 - x2^2 + x2*x3, x1^3*x3 + x1^2*x2^4 + 2*x1^2*x2^3 - x1^2*x2^2*x3 - x1^2*x2^2 - x1^2*x2*x3 - 2*x1^2*x2 + x1^2*x3 + x1^2 - 2*x1*x2^4 + x1*x2^2*x3 + 4*x1*x2^2 - x1*x2*x3 - 2*x1*x2 + x2^4 - 2*x2^3 + x2^2, x1^2*x3 - x1^2 + x1*x2^2 + x1*x2 - x1*x3 - x1 - x2^2 + x2, x1*x2^2 + x1*x2 - x1*x3 - x1 - x2^2 + x2, x1^2 - x1*x2^2 - x1*x2 + x1 + x2^2 - x2, x1^3*x2*x3 - x1^3*x2 - x1^2*x2^4 - x1^2*x2^3 + x1^2*x2^2*x3 + 2*x1^2*x2^2 + x1^2*x2 - x1^2*x3 - x1^2 + 2*x1*x2^4 - x1*x2^3 - x1*x2^2*x3 - 3*x1*x2^2 + x1*x2*x3 + 2*x1*x2 - x2^4 + 2*x2^3 - x2^2, x3 - 1, x1^2*x2^4 - x1^2*x2^3*x3 + 2*x1^2*x2^3 - 2*x1^2*x2^2*x3 - x1^2*x2^2 + x1^2*x2*x3 - 2*x1^2*x2 + x1^2*x3 + x1^2 - 2*x1*x2^4 + x1*x2^3*x3 + 4*x1*x2^2 - x1*x2*x3 - 2*x1*x2 + x2^4 - 2*x2^3 + x2^2, x1*x2 + 2*x1 - x2, x1 - 1, x1^2*x2 + x1*x2^2 - x1 - x2^2 + x2, x1 - x2, x1^2 + x1*x2^2 - x1 - x2^2 + x2, x1^2 + x1*x2^3 - 3*x1*x2 + x1 - x2^3 + 2*x2^2 - x2, x1^3*x2^2 + 2*x1^3*x2 - x1^2*x2^2 - x1^2 - x1*x2^3 - x1*x2^2 + 2*x1*x2 + x2^3 - x2^2, x1*x2^3 + 2*x1*x2^2 - x1*x2 - x1 - x2^3 + x2, x1^2 + x1*x2^3 + 2*x1*x2^2 - x1*x2 - x1 - x2^3 + x2, x1^2*x2^2 - x1^2 + x1*x2^3 - x2^3 + x2^2, x1*x2^2 - 2*x1 - x2^2 + 2*x2, x1^2*x2^2 - 2*x1^2 - 2*x1*x2^2 + x1*x2 + x1 + x2^2 - x2, x1^2*x2^2 + x1^2*x2 - 2*x1^2 - x1*x2^3 - 3*x1*x2^2 + 2*x1*x2 + x1 + x2^3 - x2, x1^3 + x1^2*x2^4 + 2*x1^2*x2^3 - 3*x1^2*x2^2 - 4*x1^2*x2 + 3*x1^2 - 2*x1*x2^4 + 6*x1*x2^2 - 4*x1*x2 + x2^4 - 2*x2^3 + x2^2, x1^3*x2 + x1^2*x2^5 + 3*x1^2*x2^4 - x1^2*x2^3 - 5*x1^2*x2^2 + x1^2*x2 + x1^2 - 2*x1*x2^5 - 2*x1*x2^4 + 6*x1*x2^3 - 2*x1*x2 + x2^5 - x2^4 - x2^3 + x2^2]