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