  We study the Borel moment map $\mu_B:T^*(\mathfrak{b}\times
\mathbb{C}^n)\rightarrow \mathfrak{b}^*$, given by $(r,s,i,j)\mapsto [r,s]+ij$,
and describe our algorithm to construct the geometric invariant theory (GIT)
quotients $\mu_B^{-1}(0)/\!\!/_{\det}B$ and $\mu_B^{-1}(0)/\!\!/_{\det^{-1}}B$,
and the affine quotient $\mu_B^{-1}(0)/\!\!/B$. We also provide an insight of
the singular locus of $2^n$ irreducible components of $\mu_B$. Finally,
analogous to the Hilbert--Chow morphism, we discuss that the GIT quotient for
the Borel setting is a resolution of singularities.
